In [1]:
import itertools
import pandas as pd
from statsmodels.tsa.statespace.sarimax import SARIMAX
import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics import mean_squared_error
import os

os.getcwd()

#df = pd.read_csv('Zip_zhvi_uc_sfr_tier_0.33_0.67_sm_sa_mon.csv')
df = pd.read_csv('Zip_zhvi_uc_sfrcondo_tier_0.33_0.67_sm_sa_month.csv')

df.head()
Out[1]:
RegionID SizeRank RegionName RegionType StateName State City Metro CountyName 2000-01-31 ... 2023-03-31 2023-04-30 2023-05-31 2023-06-30 2023-07-31 2023-08-31 2023-09-30 2023-10-31 2023-11-30 2023-12-31
0 91982 1 77494 zip TX TX Katy Houston-The Woodlands-Sugar Land, TX Fort Bend County 208752.177188 ... 468400.012962 469600.790271 471587.869725 474687.471351 477460.027392 479919.299106 481726.908022 482958.479293 483644.390919 484254.484150
1 61148 2 8701 zip NJ NJ Lakewood New York-Newark-Jersey City, NY-NJ-PA Ocean County 133799.965954 ... 517054.419786 521100.063176 526320.736228 532105.809020 538056.023382 543798.549494 549960.546654 557112.585902 563739.635747 568385.787815
2 91940 3 77449 zip TX TX Katy Houston-The Woodlands-Sugar Land, TX Harris County 102327.332899 ... 274575.011824 273391.851083 272916.706411 273291.932508 274045.370378 274933.235990 275461.772882 275451.663963 275219.130604 274931.001539
3 62080 4 11368 zip NY NY New York New York-Newark-Jersey City, NY-NJ-PA Queens County 147672.475058 ... 480340.864596 473730.902787 466644.010241 461261.507623 459443.414913 459437.482269 458881.548977 456860.171677 453514.767036 449239.710048
4 91733 5 77084 zip TX TX Houston Houston-The Woodlands-Sugar Land, TX Harris County 100957.722364 ... 267553.019024 266769.398609 266628.259422 267219.988459 268054.762069 268918.974834 269342.669492 269333.119699 268917.017812 268499.368493

5 rows × 297 columns

In [13]:
df.columns
Out[13]:
Index(['RegionID', 'SizeRank', 'RegionName', 'RegionType', 'StateName',
       'State', 'City', 'Metro', 'CountyName', '2000-01-31',
       ...
       '2023-03-31', '2023-04-30', '2023-05-31', '2023-06-30', '2023-07-31',
       '2023-08-31', '2023-09-30', '2023-10-31', '2023-11-30', '2023-12-31'],
      dtype='object', length=297)
In [14]:
df.shape
Out[14]:
(26354, 297)
In [3]:
df.iloc[:, 9:].transpose()
Out[3]:
0 1 2 3 4 5 6 7 8 9 ... 26344 26345 26346 26347 26348 26349 26350 26351 26352 26353
2000-01-31 208752.177188 133799.965954 102327.332899 147672.475058 100957.722364 89209.529378 260775.195493 153242.924036 181060.959958 112567.262934 ... NaN NaN NaN 92897.827606 NaN NaN NaN NaN NaN NaN
2000-02-29 208933.355223 134352.196216 102341.472343 149140.189415 100915.381721 89194.374796 261897.642882 153540.930524 181301.483813 113020.027694 ... NaN NaN NaN 93242.611189 NaN NaN NaN NaN NaN NaN
2000-03-31 209417.484597 134725.444700 102215.866898 150242.618161 100736.106679 89213.721442 263318.510956 153690.642549 181605.552842 113694.729026 ... NaN NaN NaN 93555.552949 NaN NaN NaN NaN NaN NaN
2000-04-30 210395.321387 135671.036962 102206.257761 152082.798879 100654.202432 89190.711160 265320.337636 154078.667948 182443.232876 114738.515131 ... NaN NaN NaN 93591.534454 NaN NaN NaN NaN NaN NaN
2000-05-31 210430.298443 136654.797404 102252.914700 153402.530230 100629.838251 89215.579690 266758.899723 154412.141624 183719.323956 115661.091881 ... NaN NaN NaN 93761.792886 NaN NaN NaN NaN NaN NaN
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
2023-08-31 479919.299106 543798.549494 274933.235990 459437.482269 268918.974834 202834.973696 794531.597036 404537.125588 657428.859504 555302.427921 ... 349103.150059 180495.338305 177392.795295 203073.135906 84201.214216 339422.454131 175266.666374 102138.167674 103008.548422 188893.327101
2023-09-30 481726.908022 549960.546654 275461.772882 458881.548977 269342.669492 203766.774891 792554.183994 402707.518398 656723.666185 562943.391380 ... 350525.216453 179971.338387 176375.701615 204330.536466 84705.676269 341345.810653 175371.383285 102509.371773 104356.053262 189526.836516
2023-10-31 482958.479293 557112.585902 275451.663963 456860.171677 269333.119699 204465.130798 791285.829718 400968.770012 655585.521751 569213.775274 ... 351066.696656 179101.409734 175829.886878 204894.639796 85641.204921 342917.881661 175565.910147 103003.798605 105233.060031 190129.583364
2023-11-30 483644.390919 563739.635747 275219.130604 453514.767036 268917.017812 204640.102855 790059.804507 399185.708326 655055.195335 574733.557641 ... 351217.036317 177946.680047 175541.800674 204736.905723 86506.384636 343768.957866 175480.717039 102776.008170 105655.210102 190661.229579
2023-12-31 484254.484150 568385.787815 274931.001539 449239.710048 268499.368493 204820.250162 789922.404553 397292.509346 656671.669776 578625.465840 ... 351324.667325 176831.704775 175871.874494 202979.091676 87050.209550 344129.353257 175335.009772 102900.456065 105737.932944 191578.956245

288 rows × 26354 columns

In [25]:
df.shape
Out[25]:
(26354, 297)
In [22]:
cutoff = round(df.shape[0]*0.9)
print("cutoff:",cutoff)
cutoff: 23719
In [4]:
import itertools
import pandas as pd
from statsmodels.tsa.statespace.sarimax import SARIMAX
import numpy as np
import matplotlib.pyplot as plt
from sklearn.metrics import mean_squared_error

def rmse(y_true, y_pred):
    return np.sqrt(mean_squared_error(y_true, y_pred))

# def format_df(df, zip_code):
#     df = df[df['RegionName'] == zip_code]
#     df = df.iloc[:, 9:].transpose()
#     df.index = pd.to_datetime(df.index, infer_datetime_format=True)
#     df = df.rename(columns={df.columns[0]: 'Zillow Home Value Index (ZHVI)'})
#     df.dropna(inplace=True)
#     df['financial_crisis_flag'] = 0
#     df.loc['2007-08-30': '2012-01-31', 'financial_crisis_flag'] = 1
#     return df

# def format_df(df, zip_code):
#     if zip_code not in df['RegionName'].values:
#         raise ValueError(f"Zip code {zip_code} not found in DataFrame.")

#     df = df[df['RegionName'] == zip_code]

#     if df.empty:
#         raise ValueError(f"No data available for zip code {zip_code}.")

#     df = df.iloc[:, 9:].transpose()
    
#     if df.empty:
#         raise ValueError(f"Transposed DataFrame is empty for zip code {zip_code}.")

#     df.index = pd.to_datetime(df.index, infer_datetime_format=True)
#     df = df.rename(columns={df.columns[0]: 'Zillow Home Value Index (ZHVI)'})
#     df.dropna(inplace=True)
#     df['financial_crisis_flag'] = 0
#     df.loc['2007-08-30': '2012-01-31', 'financial_crisis_flag'] = 1

#     return df

def format_df(df, zip_code):
    if zip_code not in df['RegionName'].values:
        raise ValueError(f"Zip code {zip_code} not found in DataFrame.")

    df = df[df['RegionName'] == zip_code]

    if df.empty:
        raise ValueError(f"No data available for zip code {zip_code}.")

    df = df.iloc[:, 9:].transpose()
    
    if df.empty:
        raise ValueError(f"Transposed DataFrame is empty for zip code {zip_code}.")

    df.index = pd.to_datetime(df.index, infer_datetime_format=True)
    df = df.rename(columns={df.columns[0]: 'Zillow Home Value Index (ZHVI)'})
    df.dropna(inplace=True)

    # Set financial_crisis_flag for original financial crisis period
    df['financial_crisis_flag'] = 0
    df.loc['2007-08-30': '2012-01-31', 'financial_crisis_flag'] = 1

    # Set financial_crisis_flag for COVID lockdown period (adjust dates as needed)
    covid_start, covid_end = '2020-03-01', '2021-06-30'
    df.loc[covid_start: covid_end, 'financial_crisis_flag'] = 1

    return df


def find_sarimax_parameters(df):
    cutoff = round(df.shape[0]*0.8)
    train = df['Zillow Home Value Index (ZHVI)'][:cutoff].dropna()
    exog = df.dropna()['financial_crisis_flag'][:cutoff]
    print("len(exog):",len(exog))

    p = q = range(0, 4)
    #d = range(0, 3)
    d=[2]
    pdq = list(itertools.product(p, d, q))
    seasonal_pdq = [(x[0], x[1], x[2], 12) for x in itertools.product([0,1], [0], [0,1])]

    results_dict = {}

    for o in pdq:
        for so in seasonal_pdq:
            try:
                model = SARIMAX(endog=train, exog=exog, order=o, seasonal_order=so, freq='M').fit()
                results_dict[(o, so)] = model.aic
            except:
                continue

    rdf = pd.DataFrame(results_dict.items(), columns=['Parameters', 'AIC'])
    return rdf.sort_values('AIC').head(20)

def model(df, order, seasonal_order, zip_code):
    try:    
        cutoff = round(df.shape[0]*0.8)
        print("cutoff:",cutoff)

        train = df['Zillow Home Value Index (ZHVI)'][:cutoff].dropna()
        print("len(train):",len(train))

        exog_train = df['financial_crisis_flag'][:cutoff]
        print("len(exog_train):",len(exog_train))

        test = df['Zillow Home Value Index (ZHVI)'][cutoff:]
        print("len(test):",len(test))

        exog_test = df['financial_crisis_flag'][cutoff:].values.reshape(-1, 1)
        print("len(exog_test):",len(exog_test))


        #Experimenting with different optimization methods (e.g., 'nm', 'bfgs', 'lbfgs', etc, and maxiter=500
        model = SARIMAX(endog=train, exog=exog_train, order=order, seasonal_order=seasonal_order, freq='M', method='lbfgs', maxiter=500).fit(disp=False)
        #model = SARIMAX(endog=train, exog=exog_train, order=order, seasonal_order=seasonal_order, freq='M').fit()


        #y_hat_train = model.predict(start=train.index[2], typ='levels')
        #y_hat_test = model.predict(start=test.index[0], end=test.index[-1], typ='levels', exog=exog_test)

        # Ensure that the index you're accessing is within the range
        if len(train.index) > 2 and len(test.index) > 0:
            y_hat_train = model.predict(start=train.index[2], typ='levels')
            y_hat_test = model.predict(start=test.index[0], end=test.index[-1], typ='levels', exog=exog_test)
        else:
            raise IndexError("Insufficient data points for prediction.")


        print(model.summary())
        print(f'Test RMSE: {rmse(test, y_hat_test)}')
        print(f'Parameters Used: {order, seasonal_order}')

        fig, ax = plt.subplots(figsize=(12,8))
        ax.plot(train, label='train')
        ax.plot(test, label='test')
        ax.plot(y_hat_train, label='train prediction')
        ax.plot(y_hat_test, label='test prediction')
        ax.set_ylabel('Zillow Home Value Index (ZHVI)', fontsize=12)
        ax.set_xlabel('Year', fontsize=12)
        ax.set_title(f"ZHVI Forecasting for Zip Code {zip_code}")  # Include ZIP code in title
        plt.legend()
        plt.show()

        test_rmse = rmse(test, y_hat_test)
        #forecast_steps = len(test)
        #exog_forecast = np.zeros(forecast_steps).reshape(-1, 1) 

        # Use len(test) for forecast steps
        forecast_steps = len(test)  
        exog_forecast_length = len(exog_test)

        exog_forecast = np.zeros(forecast_steps).reshape(-1, 1) 

        # If exog_test has observations, use them for the initial part of the forecast
        if exog_forecast_length > 0:
            exog_forecast[:exog_forecast_length] = exog_test


        print("len(exog_forecast) Forecast time period in months:",len(exog_forecast))

        #forecast = model.forecast(steps=forecast_steps, exog=exog_forecast)
        forecast = model.forecast(steps=forecast_steps, exog=exog_forecast)

        # Last observed value in the TRAIN set
        last_train_value = train.iloc[-1]
        forecast_return = (forecast[-1] - last_train_value) / last_train_value * 100   

        return test_rmse, forecast_return
    
    except (ValueError, IndexError) as e:
        # Handle the error appropriately
        print(f"Error processing ZIP Code {zip_code}: {e}. Skipping...")
        return None, None 

def select_parameters_with_lowest_order(best_params_df):
    # Adding a new column for the sum of orders
    best_params_df['order_sum'] = best_params_df['Parameters'].apply(lambda x: sum(x[0]) + sum(x[1]))

    # Sorting first by AIC, then by order sum
    sorted_params = best_params_df.sort_values(by=['AIC', 'order_sum'])

    # Selecting the parameters with the lowest sum of orders
    selected_params = sorted_params.iloc[0]['Parameters']
    return selected_params

# def aggregate_results(zip_codes, df):
#     results = []
#     for zip_code in zip_codes:
#         if zip_code not in df['RegionName'].values:
#             print(f"Zip code {zip_code} not found in DataFrame. Skipping...")
#             continue

#         formatted_df = format_df(df, zip_code)
#         best_params_df = find_sarimax_parameters(formatted_df)

#         # Check if best_params_df is not empty before proceeding
#         if best_params_df.empty:
#             print(f"No suitable model parameters found for ZIP Code {zip_code}. Skipping...")
#             continue

#         best_order, best_seasonal_order = select_parameters_with_lowest_order(best_params_df)
#         test_rmse, forecast_return = model(formatted_df, best_order, best_seasonal_order, zip_code)
#         results.append({'Zip_Code': zip_code, 'Test_RMSE': test_rmse, 'Forecast_%_Appreciation': forecast_return, 'Parameters Used': best_order + best_seasonal_order})

#     return pd.DataFrame(results)

def aggregate_results(zip_codes, df):
    results = []
    for zip_code in zip_codes:
        try:
            if zip_code not in df['RegionName'].values:
                print(f"Zip code {zip_code} not found in DataFrame. Skipping...")
                continue

            formatted_df = format_df(df, zip_code)
            best_params_df = find_sarimax_parameters(formatted_df)

            # Check if best_params_df is not empty before proceeding
            if best_params_df.empty:
                print(f"No suitable model parameters found for ZIP Code {zip_code}. Skipping...")
                continue

            best_order, best_seasonal_order = select_parameters_with_lowest_order(best_params_df)
            test_rmse, forecast_return = model(formatted_df, best_order, best_seasonal_order, zip_code)
            results.append({'Zip_Code': zip_code, 'Test_RMSE': test_rmse, 'Forecast_%_Appreciation': forecast_return, 'Parameters Used': best_order + best_seasonal_order})

        except Exception as e:  # Catching any kind of exception
            print(f"Error processing ZIP Code {zip_code}: {e}. Skipping...")
            continue

    return pd.DataFrame(results)
In [5]:
## Updated version above!
In [6]:
# #zip_codes = [23120, 23112, 23224, 23832, 23238]
# zip_codes = [23103, 23106]
# results_df = aggregate_results(zip_codes, df)
# print(results_df)
In [7]:
# print(results_df)
In [8]:
# df[df['State'] == 'VA']['RegionName']
In [9]:
# df['RegionName'][:5]
In [10]:
# zip_codes = df[df['State'] == 'VA']['RegionName'][:5]
# results_df = aggregate_results(zip_codes, df)
In [11]:
# print(results_df)
In [12]:
# results_df
In [13]:
import geopandas as gpd
import matplotlib.pyplot as plt

# Step 1: Read the shapefile
shapefile_path_bkg = 'C:\\Users\\rsingh\\OneDrive - PlanRVA\\Documents\\DataHub-Rishabh\\Default Shapefiles\\va_zipcodes\\va-Zipcodes_RTC_PlanRVA.shp'  # Update with the path to your shapefile
#Planrva_file_Above
shapefile_path = 'C:\\Users\\rsingh\\OneDrive - PlanRVA\\Documents\\DataHub-Rishabh\\Default Shapefiles\\va_zipcodes\\tl_2019_us_zcta510\\tl_2019_us_zcta510.shp'
gdf = gpd.read_file(shapefile_path)
#When Planrva is the footprint 
gdf_bkg = gpd.read_file(shapefile_path_bkg)
gdf.head()
Out[13]:
ZCTA5CE10 GEOID10 CLASSFP10 MTFCC10 FUNCSTAT10 ALAND10 AWATER10 INTPTLAT10 INTPTLON10 geometry
0 43451 43451 B5 G6350 S 63484186 157689 +41.3183010 -083.6174935 POLYGON ((-83.70873 41.32733, -83.70815 41.327...
1 43452 43452 B5 G6350 S 121522304 13721730 +41.5157923 -082.9809454 POLYGON ((-83.08698 41.53780, -83.08256 41.537...
2 43456 43456 B5 G6350 S 9320975 1003775 +41.6318300 -082.8393923 MULTIPOLYGON (((-82.83558 41.71082, -82.83515 ...
3 43457 43457 B5 G6350 S 48004681 0 +41.2673301 -083.4274872 POLYGON ((-83.49650 41.25371, -83.48382 41.253...
4 43458 43458 B5 G6350 S 2573816 39915 +41.5304461 -083.2133648 POLYGON ((-83.22229 41.53102, -83.22228 41.532...
In [14]:
## PlanRVA region Zipcodes
zip_codes = gdf_bkg['GEOID10'].astype(int)
In [15]:
zip_codes
Out[15]:
0     23089
1     23093
2     23102
3     23103
4     23106
      ...  
80    23038
81    23039
82    23047
83    23059
84    23060
Name: GEOID10, Length: 85, dtype: int32
In [16]:
# Rename 'old_column_name' to 'new_column_name'
gdf.rename(columns={'GEOID10': 'Zip_Code'}, inplace=True)
In [17]:
df.columns
Out[17]:
Index(['RegionID', 'SizeRank', 'RegionName', 'RegionType', 'StateName',
       'State', 'City', 'Metro', 'CountyName', '2000-01-31',
       ...
       '2023-03-31', '2023-04-30', '2023-05-31', '2023-06-30', '2023-07-31',
       '2023-08-31', '2023-09-30', '2023-10-31', '2023-11-30', '2023-12-31'],
      dtype='object', length=297)
In [18]:
## Run model on desired df
results_df = aggregate_results(zip_codes, df)
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 1)   Log Likelihood               -1765.779
Date:                            Sat, 27 Jan 2024   AIC                           3541.559
Time:                                    01:35:47   BIC                           3558.706
Sample:                                01-31-2000   HQIC                          3548.477
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    65.2649    511.953      0.127      0.899    -938.145    1068.675
ar.L1                     0.5859      0.314      1.868      0.062      -0.029       1.201
ar.L2                    -0.0649      0.019     -3.421      0.001      -0.102      -0.028
ma.L1                    -0.5617      0.314     -1.791      0.073      -1.177       0.053
sigma2                 3.009e+05   1.15e+04     26.197      0.000    2.78e+05    3.23e+05
===================================================================================
Ljung-Box (L1) (Q):                  11.36   Jarque-Bera (JB):              1931.19
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.11   Skew:                            -1.33
Prob(H) (two-sided):                  0.00   Kurtosis:                        17.01
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 33254.056059205395
Parameters Used: ((2, 2, 1), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 144
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 144
len(train): 144
len(exog_train): 144
len(test): 36
len(exog_test): 36
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  144
Model:                           SARIMAX(2, 2, 3)   Log Likelihood               -1003.760
Date:                            Sat, 27 Jan 2024   AIC                           2021.520
Time:                                    01:36:05   BIC                           2042.210
Sample:                                01-31-2009   HQIC                          2029.928
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    62.9444    179.088      0.351      0.725    -288.062     413.951
ar.L1                     0.9536      0.062     15.481      0.000       0.833       1.074
ar.L2                    -0.9146      0.059    -15.554      0.000      -1.030      -0.799
ma.L1                    -0.9254      0.083    -11.085      0.000      -1.089      -0.762
ma.L2                     0.9190      0.074     12.360      0.000       0.773       1.065
ma.L3                    -0.0055      0.056     -0.100      0.921      -0.114       0.103
sigma2                 8.435e+04   8538.976      9.879      0.000    6.76e+04    1.01e+05
===================================================================================
Ljung-Box (L1) (Q):                   4.55   Jarque-Bera (JB):                17.26
Prob(Q):                              0.03   Prob(JB):                         0.00
Heteroskedasticity (H):               2.59   Skew:                             0.52
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.35
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 39470.57837042498
Parameters Used: ((2, 2, 3), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 144
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 144
len(train): 144
len(exog_train): 144
len(test): 36
len(exog_test): 36
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  144
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1064.985
Date:                            Sat, 27 Jan 2024   AIC                           2141.970
Time:                                    01:36:33   BIC                           2159.705
Sample:                                01-31-2009   HQIC                          2149.176
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   225.1185    168.794      1.334      0.182    -105.712     555.949
ar.L1                     0.6801      0.213      3.188      0.001       0.262       1.098
ar.L2                    -0.7740      0.171     -4.516      0.000      -1.110      -0.438
ma.L1                    -0.6488      0.218     -2.981      0.003      -1.075      -0.222
ma.L2                     0.7727      0.168      4.587      0.000       0.443       1.103
sigma2                 1.538e+05    1.5e+04     10.276      0.000    1.24e+05    1.83e+05
===================================================================================
Ljung-Box (L1) (Q):                  17.54   Jarque-Bera (JB):                 1.14
Prob(Q):                              0.00   Prob(JB):                         0.57
Heteroskedasticity (H):               2.92   Skew:                             0.01
Prob(H) (two-sided):                  0.00   Kurtosis:                         3.44
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 63255.21646616508
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 142
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 142
len(train): 142
len(exog_train): 142
len(test): 35
len(exog_test): 35
Error processing ZIP Code 23103: Provided exogenous values are not of the appropriate shape. Required (38, 1), got (35, 1).. Skipping...
len(exog): 145
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 145
len(train): 145
len(exog_train): 145
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  145
Model:                           SARIMAX(3, 2, 2)   Log Likelihood               -1089.682
Date:                            Sat, 27 Jan 2024   AIC                           2193.365
Time:                                    01:37:30   BIC                           2214.105
Sample:                                12-31-2008   HQIC                          2201.792
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    79.4854    245.137      0.324      0.746    -400.974     559.945
ar.L1                     1.0907      0.026     42.620      0.000       1.041       1.141
ar.L2                    -1.0207      0.024    -43.318      0.000      -1.067      -0.975
ar.L3                     0.0203      0.021      0.987      0.324      -0.020       0.061
ma.L1                    -1.0663      0.043    -24.543      0.000      -1.152      -0.981
ma.L2                     0.9988      0.080     12.503      0.000       0.842       1.155
sigma2                  1.67e+05      0.075   2.24e+06      0.000    1.67e+05    1.67e+05
===================================================================================
Ljung-Box (L1) (Q):                  11.55   Jarque-Bera (JB):                52.95
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.51   Skew:                             0.20
Prob(H) (two-sided):                  0.02   Kurtosis:                         5.95
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 3.96e+22. Standard errors may be unstable.
Test RMSE: 28930.36766221483
Parameters Used: ((3, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
len(exog_forecast) Forecast time period in months: 36
len(exog): 212
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 212
len(train): 212
len(exog_train): 212
len(test): 53
len(exog_test): 53
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  212
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1548.192
Date:                            Sat, 27 Jan 2024   AIC                           3108.384
Time:                                    01:37:56   BIC                           3128.467
Sample:                                12-31-2001   HQIC                          3116.503
                                     - 07-31-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   199.8067     77.217      2.588      0.010      48.464     351.150
ar.L1                     0.4478      0.067      6.654      0.000       0.316       0.580
ar.L2                    -0.8832      0.065    -13.660      0.000      -1.010      -0.756
ma.L1                    -0.4285      0.077     -5.563      0.000      -0.579      -0.278
ma.L2                     0.8457      0.075     11.333      0.000       0.699       0.992
sigma2                 1.303e+05   8490.472     15.348      0.000    1.14e+05    1.47e+05
===================================================================================
Ljung-Box (L1) (Q):                   4.26   Jarque-Bera (JB):               117.70
Prob(Q):                              0.04   Prob(JB):                         0.00
Heteroskedasticity (H):               0.72   Skew:                             0.16
Prob(H) (two-sided):                  0.18   Kurtosis:                         6.65
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 44967.4193534858
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 53
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1691.126
Date:                            Sat, 27 Jan 2024   AIC                           3394.253
Time:                                    01:38:25   BIC                           3414.829
Sample:                                01-31-2000   HQIC                          3402.555
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -154.5489    145.115     -1.065      0.287    -438.970     129.872
ar.L1                     1.0733      0.009    113.938      0.000       1.055       1.092
ar.L2                    -0.9955      0.009   -106.533      0.000      -1.014      -0.977
ma.L1                    -1.0654      0.015    -72.723      0.000      -1.094      -1.037
ma.L2                     0.9946      0.028     36.112      0.000       0.941       1.049
sigma2                 1.466e+05   9533.018     15.376      0.000    1.28e+05    1.65e+05
===================================================================================
Ljung-Box (L1) (Q):                  14.14   Jarque-Bera (JB):               131.70
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.22   Skew:                             0.35
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.66
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 29736.680912999862
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 229
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 229
len(train): 229
len(exog_train): 229
len(test): 57
len(exog_test): 57
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
Error processing ZIP Code 23113: Provided exogenous values are not of the appropriate shape. Required (59, 1), got (57, 1).. Skipping...
len(exog): 230
No suitable model parameters found for ZIP Code 23114. Skipping...
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1744.058
Date:                            Sat, 27 Jan 2024   AIC                           3500.117
Time:                                    01:39:19   BIC                           3520.693
Sample:                                01-31-2000   HQIC                          3508.419
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   186.6021     93.237      2.001      0.045       3.861     369.343
ar.L1                     0.5168      0.011     45.191      0.000       0.494       0.539
ar.L2                    -0.9968      0.010    -99.709      0.000      -1.016      -0.977
ma.L1                    -0.5220      0.017    -29.915      0.000      -0.556      -0.488
ma.L2                     0.9956      0.024     41.810      0.000       0.949       1.042
sigma2                 2.291e+05   1.42e+04     16.183      0.000    2.01e+05    2.57e+05
===================================================================================
Ljung-Box (L1) (Q):                  14.06   Jarque-Bera (JB):               117.62
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.91   Skew:                             0.28
Prob(H) (two-sided):                  0.67   Kurtosis:                         6.47
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 9.27e+14. Standard errors may be unstable.
Test RMSE: 47943.43843315045
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 211
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 211
len(train): 211
len(exog_train): 211
len(test): 53
len(exog_test): 53
Error processing ZIP Code 23117: Provided exogenous values are not of the appropriate shape. Required (55, 1), got (53, 1).. Skipping...
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 57
len(exog_test): 57
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1872.245
Date:                            Sat, 27 Jan 2024   AIC                           3756.490
Time:                                    01:40:02   BIC                           3777.066
Sample:                                02-29-2000   HQIC                          3764.791
                                     - 03-31-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -85.4367   3352.484     -0.025      0.980   -6656.184    6485.311
ar.L1                     0.7330      0.012     60.107      0.000       0.709       0.757
ar.L2                    -0.9658      0.014    -69.628      0.000      -0.993      -0.939
ma.L1                    -0.7213      0.013    -57.248      0.000      -0.746      -0.697
ma.L2                     0.9712      0.013     73.263      0.000       0.945       0.997
sigma2                 7.328e+05   4.16e+04     17.626      0.000    6.51e+05    8.14e+05
===================================================================================
Ljung-Box (L1) (Q):                  12.12   Jarque-Bera (JB):               179.77
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.20   Skew:                             0.38
Prob(H) (two-sided):                  0.00   Kurtosis:                         7.28
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 21834.006062146007
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 57
len(exog): 146
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 146
len(train): 146
len(exog_train): 146
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  146
Model:                           SARIMAX(2, 2, 0)   Log Likelihood               -1029.552
Date:                            Sat, 27 Jan 2024   AIC                           2067.104
Time:                                    01:40:24   BIC                           2078.983
Sample:                                11-30-2008   HQIC                          2071.931
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   133.3627    168.292      0.792      0.428    -196.483     463.208
ar.L1                     0.0232      0.017      1.405      0.160      -0.009       0.056
ar.L2                     0.0407      0.033      1.240      0.215      -0.024       0.105
sigma2                 9.261e+04   1.08e+04      8.611      0.000    7.15e+04    1.14e+05
===================================================================================
Ljung-Box (L1) (Q):                  24.10   Jarque-Bera (JB):                 3.71
Prob(Q):                              0.00   Prob(JB):                         0.16
Heteroskedasticity (H):               1.14   Skew:                             0.39
Prob(H) (two-sided):                  0.66   Kurtosis:                         3.10
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 42688.16352510824
Parameters Used: ((2, 2, 0), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 75
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 75
len(train): 75
len(exog_train): 75
len(test): 19
len(exog_test): 19
Error processing ZIP Code 23129: Provided exogenous values are not of the appropriate shape. Required (21, 1), got (19, 1).. Skipping...
len(exog): 157
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 157
len(train): 157
len(exog_train): 157
len(test): 39
len(exog_test): 39
                                      SARIMAX Results                                       
============================================================================================
Dep. Variable:       Zillow Home Value Index (ZHVI)   No. Observations:                  157
Model:             SARIMAX(3, 2, 2)x(1, 0, [1], 12)   Log Likelihood               -1134.817
Date:                              Sat, 27 Jan 2024   AIC                           2287.635
Time:                                      01:41:08   BIC                           2315.025
Sample:                                  09-30-2007   HQIC                          2298.760
                                       - 09-30-2020                                         
Covariance Type:                                opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    40.0538    536.240      0.075      0.940   -1010.957    1091.064
ar.L1                     1.7656      0.018     95.988      0.000       1.730       1.802
ar.L2                    -1.0268      0.024    -42.803      0.000      -1.074      -0.980
ar.L3                     0.0211      0.013      1.672      0.095      -0.004       0.046
ma.L1                    -1.7498      0.019    -91.255      0.000      -1.787      -1.712
ma.L2                     0.9902      0.017     57.463      0.000       0.956       1.024
ar.S.L12                  0.7789      0.366      2.127      0.033       0.061       1.497
ma.S.L12                 -0.7937      0.357     -2.221      0.026      -1.494      -0.093
sigma2                 1.351e+05      0.264   5.11e+05      0.000    1.35e+05    1.35e+05
===================================================================================
Ljung-Box (L1) (Q):                  27.66   Jarque-Bera (JB):                 2.66
Prob(Q):                              0.00   Prob(JB):                         0.26
Heteroskedasticity (H):               2.18   Skew:                            -0.01
Prob(H) (two-sided):                  0.01   Kurtosis:                         3.64
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 1.84e+22. Standard errors may be unstable.
Test RMSE: 37674.07472813267
Parameters Used: ((3, 2, 2), (1, 0, 1, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 39
len(exog): 146
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 146
len(train): 146
len(exog_train): 146
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  146
Model:                           SARIMAX(2, 2, 0)   Log Likelihood               -1055.530
Date:                            Sat, 27 Jan 2024   AIC                           2119.060
Time:                                    01:41:30   BIC                           2130.939
Sample:                                11-30-2008   HQIC                          2123.887
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   149.1437    270.322      0.552      0.581    -380.678     678.965
ar.L1                     0.0413      0.017      2.436      0.015       0.008       0.075
ar.L2                     0.0340      0.064      0.533      0.594      -0.091       0.159
sigma2                 1.157e+05   1.12e+04     10.342      0.000    9.37e+04    1.38e+05
===================================================================================
Ljung-Box (L1) (Q):                  18.71   Jarque-Bera (JB):                 1.46
Prob(Q):                              0.00   Prob(JB):                         0.48
Heteroskedasticity (H):               1.27   Skew:                             0.20
Prob(H) (two-sided):                  0.41   Kurtosis:                         3.30
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 39105.53666320717
Parameters Used: ((2, 2, 0), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 146
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 146
len(train): 146
len(exog_train): 146
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  146
Model:                           SARIMAX(0, 2, 2)   Log Likelihood               -1027.466
Date:                            Sat, 27 Jan 2024   AIC                           2062.931
Time:                                    01:41:54   BIC                           2074.811
Sample:                                11-30-2008   HQIC                          2067.758
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   163.9680    219.550      0.747      0.455    -266.342     594.278
ma.L1                     0.0253      0.018      1.415      0.157      -0.010       0.060
ma.L2                     0.0351      0.047      0.743      0.458      -0.058       0.128
sigma2                  9.04e+04   1.02e+04      8.847      0.000    7.04e+04     1.1e+05
===================================================================================
Ljung-Box (L1) (Q):                  20.09   Jarque-Bera (JB):                 1.48
Prob(Q):                              0.00   Prob(JB):                         0.48
Heteroskedasticity (H):               1.80   Skew:                             0.21
Prob(H) (two-sided):                  0.04   Kurtosis:                         3.27
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 29592.794490436383
Parameters Used: ((0, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 57
len(exog_test): 57
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1833.471
Date:                            Sat, 27 Jan 2024   AIC                           3678.941
Time:                                    01:42:29   BIC                           3699.518
Sample:                                02-29-2000   HQIC                          3687.243
                                     - 03-31-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   212.0355    155.190      1.366      0.172     -92.132     516.203
ar.L1                     0.5916      0.010     58.139      0.000       0.572       0.612
ar.L2                    -0.9862      0.009   -106.713      0.000      -1.004      -0.968
ma.L1                    -0.5894      0.014    -41.849      0.000      -0.617      -0.562
ma.L2                     0.9766      0.012     79.691      0.000       0.953       1.001
sigma2                 4.162e+05   2.54e+04     16.404      0.000    3.67e+05    4.66e+05
===================================================================================
Ljung-Box (L1) (Q):                  13.76   Jarque-Bera (JB):                 8.67
Prob(Q):                              0.00   Prob(JB):                         0.01
Heteroskedasticity (H):               0.37   Skew:                             0.04
Prob(H) (two-sided):                  0.00   Kurtosis:                         3.95
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 25424.171138904305
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 57
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 3)   Log Likelihood               -1604.073
Date:                            Sat, 27 Jan 2024   AIC                           3218.145
Time:                                    01:42:53   BIC                           3235.292
Sample:                                01-31-2000   HQIC                          3225.063
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -39.0368     72.267     -0.540      0.589    -180.678     102.604
ma.L1                     0.0494      0.039      1.266      0.205      -0.027       0.126
ma.L2                    -0.0425      0.048     -0.877      0.380      -0.138       0.052
ma.L3                    -0.1424      0.014     -9.839      0.000      -0.171      -0.114
sigma2                 6.897e+04   5239.010     13.165      0.000    5.87e+04    7.92e+04
===================================================================================
Ljung-Box (L1) (Q):                   0.52   Jarque-Bera (JB):                17.87
Prob(Q):                              0.47   Prob(JB):                         0.00
Heteroskedasticity (H):               0.54   Skew:                            -0.26
Prob(H) (two-sided):                  0.01   Kurtosis:                         4.27
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 33610.62790073567
Parameters Used: ((0, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 144
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 144
len(train): 144
len(exog_train): 144
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  144
Model:             SARIMAX(0, 2, 1)x(1, 0, 1, 12)   Log Likelihood               -1072.449
Date:                            Sat, 27 Jan 2024   AIC                           2154.898
Time:                                    01:43:17   BIC                           2169.677
Sample:                                01-31-2009   HQIC                          2160.903
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   367.3267    327.475      1.122      0.262    -274.512    1009.166
ma.L1                     0.0246      0.022      1.121      0.262      -0.018       0.067
ar.S.L12                  0.8624      0.174      4.965      0.000       0.522       1.203
ma.S.L12                 -0.8753      0.164     -5.341      0.000      -1.197      -0.554
sigma2                 2.089e+05   2.63e+04      7.941      0.000    1.57e+05    2.61e+05
===================================================================================
Ljung-Box (L1) (Q):                  14.41   Jarque-Bera (JB):                 0.14
Prob(Q):                              0.00   Prob(JB):                         0.93
Heteroskedasticity (H):               2.24   Skew:                             0.07
Prob(H) (two-sided):                  0.01   Kurtosis:                         2.92
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 91127.72516365987
Parameters Used: ((0, 2, 1), (1, 0, 1, 12))
len(exog_forecast) Forecast time period in months: 36
Zip code 23160 not found in DataFrame. Skipping...
Zip code 23173 not found in DataFrame. Skipping...
len(exog): 145
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 145
len(train): 145
len(exog_train): 145
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  145
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1006.726
Date:                            Sat, 27 Jan 2024   AIC                           2025.452
Time:                                    01:43:42   BIC                           2043.229
Sample:                                12-31-2008   HQIC                          2032.676
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    -5.9134    193.315     -0.031      0.976    -384.804     372.977
ar.L1                     1.0555      0.009    116.504      0.000       1.038       1.073
ar.L2                    -0.9933      0.010   -103.331      0.000      -1.012      -0.974
ma.L1                    -1.0431      0.017    -61.476      0.000      -1.076      -1.010
ma.L2                     0.9932      0.027     37.250      0.000       0.941       1.045
sigma2                 7.409e+04   9532.748      7.772      0.000    5.54e+04    9.28e+04
===================================================================================
Ljung-Box (L1) (Q):                  12.68   Jarque-Bera (JB):                14.71
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               1.14   Skew:                            -0.30
Prob(H) (two-sided):                  0.65   Kurtosis:                         4.45
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 19091.18116014279
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 36
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1709.592
Date:                            Sat, 27 Jan 2024   AIC                           3431.184
Time:                                    01:44:12   BIC                           3451.760
Sample:                                01-31-2000   HQIC                          3439.486
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -523.0353    273.319     -1.914      0.056   -1058.731      12.661
ar.L1                     1.0917      0.010    112.901      0.000       1.073       1.111
ar.L2                    -0.9868      0.010    -99.647      0.000      -1.006      -0.967
ma.L1                    -1.0810      0.015    -74.233      0.000      -1.110      -1.052
ma.L2                     0.9757      0.015     63.061      0.000       0.945       1.006
sigma2                 1.844e+05   1.13e+04     16.390      0.000    1.62e+05    2.06e+05
===================================================================================
Ljung-Box (L1) (Q):                  13.55   Jarque-Bera (JB):                85.84
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.29   Skew:                             0.03
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.01
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 57824.348655149006
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 58
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:                           SARIMAX(2, 2, 2)   Log Likelihood                -865.731
Date:                            Sat, 27 Jan 2024   AIC                           1743.461
Time:                                    01:44:38   BIC                           1759.826
Sample:                                01-31-2012   HQIC                          1750.102
                                     - 07-31-2021                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   674.7112    222.246      3.036      0.002     239.117    1110.306
ar.L1                    -1.8108      0.027    -67.831      0.000      -1.863      -1.759
ar.L2                    -0.8965      0.025    -35.796      0.000      -0.946      -0.847
ma.L1                     1.8753      0.037     50.574      0.000       1.803       1.948
ma.L2                     0.9803      0.038     25.665      0.000       0.905       1.055
sigma2                 2.587e+05      0.374   6.91e+05      0.000    2.59e+05    2.59e+05
===================================================================================
Ljung-Box (L1) (Q):                   6.82   Jarque-Bera (JB):                 2.77
Prob(Q):                              0.01   Prob(JB):                         0.25
Heteroskedasticity (H):               0.65   Skew:                             0.05
Prob(H) (two-sided):                  0.18   Kurtosis:                         3.76
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 1.27e+23. Standard errors may be unstable.
Test RMSE: 5529.342245454633
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 29
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:                           SARIMAX(2, 2, 3)   Log Likelihood                -824.936
Date:                            Sat, 27 Jan 2024   AIC                           1663.871
Time:                                    01:44:59   BIC                           1682.963
Sample:                                01-31-2012   HQIC                          1671.619
                                     - 07-31-2021                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   452.3290    107.476      4.209      0.000     241.680     662.978
ar.L1                     0.3452      0.064      5.394      0.000       0.220       0.471
ar.L2                    -0.9001      0.087    -10.358      0.000      -1.070      -0.730
ma.L1                    -0.3405      0.079     -4.320      0.000      -0.495      -0.186
ma.L2                     0.8977      0.094      9.516      0.000       0.713       1.083
ma.L3                    -0.0303      0.045     -0.667      0.505      -0.119       0.059
sigma2                 1.284e+05   1.56e+04      8.209      0.000    9.78e+04    1.59e+05
===================================================================================
Ljung-Box (L1) (Q):                   3.00   Jarque-Bera (JB):                 4.40
Prob(Q):                              0.08   Prob(JB):                         0.11
Heteroskedasticity (H):               3.49   Skew:                             0.22
Prob(H) (two-sided):                  0.00   Kurtosis:                         3.86
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 7112.799389424293
Parameters Used: ((2, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 29
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 3)   Log Likelihood               -1596.301
Date:                            Sat, 27 Jan 2024   AIC                           3202.601
Time:                                    01:45:27   BIC                           3219.748
Sample:                                01-31-2000   HQIC                          3209.519
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -31.0647     68.351     -0.454      0.649    -165.030     102.900
ma.L1                     0.1684      0.023      7.185      0.000       0.122       0.214
ma.L2                    -0.0405      0.047     -0.859      0.390      -0.133       0.052
ma.L3                    -0.1774      0.019     -9.337      0.000      -0.215      -0.140
sigma2                 5.805e+04   4435.900     13.087      0.000    4.94e+04    6.67e+04
===================================================================================
Ljung-Box (L1) (Q):                   5.53   Jarque-Bera (JB):                92.06
Prob(Q):                              0.02   Prob(JB):                         0.00
Heteroskedasticity (H):               0.41   Skew:                            -0.72
Prob(H) (two-sided):                  0.00   Kurtosis:                         5.76
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 25110.122768031284
Parameters Used: ((0, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(1, 2, 3)   Log Likelihood               -1616.627
Date:                            Sat, 27 Jan 2024   AIC                           3245.254
Time:                                    01:45:52   BIC                           3265.830
Sample:                                01-31-2000   HQIC                          3253.556
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   117.3738     92.246      1.272      0.203     -63.426     298.173
ar.L1                     0.4009      0.077      5.207      0.000       0.250       0.552
ma.L1                    -0.0191      0.088     -0.217      0.828      -0.192       0.154
ma.L2                     0.0316      0.050      0.635      0.526      -0.066       0.129
ma.L3                    -0.4499      0.026    -17.130      0.000      -0.501      -0.398
sigma2                 5.343e+04   4720.714     11.319      0.000    4.42e+04    6.27e+04
===================================================================================
Ljung-Box (L1) (Q):                   4.13   Jarque-Bera (JB):                49.64
Prob(Q):                              0.04   Prob(JB):                         0.00
Heteroskedasticity (H):               0.89   Skew:                            -0.05
Prob(H) (two-sided):                  0.62   Kurtosis:                         5.28
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 18024.145008178763
Parameters Used: ((1, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                      SARIMAX Results                                       
============================================================================================
Dep. Variable:       Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:             SARIMAX(0, 2, 3)x(1, 0, [1], 12)   Log Likelihood               -1655.443
Date:                              Sat, 27 Jan 2024   AIC                           3324.885
Time:                                      01:46:20   BIC                           3348.891
Sample:                                  01-31-2000   HQIC                          3334.571
                                       - 02-28-2019                                         
Covariance Type:                                opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -39.5047    129.396     -0.305      0.760    -293.117     214.107
ma.L1                     0.0824      0.016      5.055      0.000       0.050       0.114
ma.L2                    -0.0160      0.041     -0.388      0.698      -0.097       0.065
ma.L3                    -0.0820      0.016     -5.291      0.000      -0.112      -0.052
ar.S.L12                 -0.9451      0.021    -44.206      0.000      -0.987      -0.903
ma.S.L12                  0.9998      0.069     14.576      0.000       0.865       1.134
sigma2                  1.07e+05      0.005   1.96e+07      0.000    1.07e+05    1.07e+05
===================================================================================
Ljung-Box (L1) (Q):                  13.96   Jarque-Bera (JB):                34.31
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               1.95   Skew:                             0.35
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.77
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 2.4e+25. Standard errors may be unstable.
Test RMSE: 25460.337724734865
Parameters Used: ((0, 2, 3), (1, 0, 1, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                      SARIMAX Results                                      
===========================================================================================
Dep. Variable:      Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:             SARIMAX(2, 2, 2)x(1, 0, [], 12)   Log Likelihood               -1718.221
Date:                             Sat, 27 Jan 2024   AIC                           3450.442
Time:                                     01:46:46   BIC                           3474.448
Sample:                                 01-31-2000   HQIC                          3460.128
                                      - 02-28-2019                                         
Covariance Type:                               opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -16.7100    121.300     -0.138      0.890    -254.453     221.033
ar.L1                     1.0947      0.173      6.331      0.000       0.756       1.434
ar.L2                    -0.7839      0.169     -4.652      0.000      -1.114      -0.454
ma.L1                    -1.0725      0.181     -5.920      0.000      -1.428      -0.717
ma.L2                     0.7425      0.177      4.200      0.000       0.396       1.089
ar.S.L12                  0.0221      0.049      0.448      0.654      -0.075       0.119
sigma2                 1.984e+05   1.63e+04     12.172      0.000    1.66e+05     2.3e+05
===================================================================================
Ljung-Box (L1) (Q):                  22.99   Jarque-Bera (JB):                10.22
Prob(Q):                              0.00   Prob(JB):                         0.01
Heteroskedasticity (H):               2.08   Skew:                             0.30
Prob(H) (two-sided):                  0.00   Kurtosis:                         3.84
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 18668.54109035659
Parameters Used: ((2, 2, 2), (1, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 3)   Log Likelihood               -1636.154
Date:                            Sat, 27 Jan 2024   AIC                           3282.309
Time:                                    01:47:14   BIC                           3299.456
Sample:                                01-31-2000   HQIC                          3289.227
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -30.5474     54.904     -0.556      0.578    -138.156      77.062
ma.L1                     0.0465      0.017      2.662      0.008       0.012       0.081
ma.L2                    -0.0451      0.051     -0.879      0.379      -0.146       0.055
ma.L3                    -0.0993      0.013     -7.497      0.000      -0.125      -0.073
sigma2                 9.155e+04   6972.085     13.131      0.000    7.79e+04    1.05e+05
===================================================================================
Ljung-Box (L1) (Q):                  12.66   Jarque-Bera (JB):                12.47
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.92   Skew:                             0.19
Prob(H) (two-sided):                  0.72   Kurtosis:                         4.08
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 29763.17510465127
Parameters Used: ((0, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 3)   Log Likelihood               -1664.323
Date:                            Sat, 27 Jan 2024   AIC                           3338.647
Time:                                    01:47:41   BIC                           3355.793
Sample:                                01-31-2000   HQIC                          3345.565
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -103.0634    103.453     -0.996      0.319    -305.827      99.701
ma.L1                     0.0820      0.022      3.743      0.000       0.039       0.125
ma.L2                     0.0006      0.040      0.015      0.988      -0.077       0.078
ma.L3                    -0.1255      0.014     -8.932      0.000      -0.153      -0.098
sigma2                 1.158e+05   5935.593     19.517      0.000    1.04e+05    1.27e+05
===================================================================================
Ljung-Box (L1) (Q):                   4.39   Jarque-Bera (JB):               287.52
Prob(Q):                              0.04   Prob(JB):                         0.00
Heteroskedasticity (H):               1.01   Skew:                             0.55
Prob(H) (two-sided):                  0.95   Kurtosis:                         8.39
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 17958.11242591756
Parameters Used: ((0, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 227
No suitable model parameters found for ZIP Code 23229. Skipping...
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 3)   Log Likelihood               -1661.882
Date:                            Sat, 27 Jan 2024   AIC                           3333.764
Time:                                    01:48:08   BIC                           3350.911
Sample:                                01-31-2000   HQIC                          3340.682
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -34.3886     98.839     -0.348      0.728    -228.109     159.332
ma.L1                     0.0528      0.019      2.788      0.005       0.016       0.090
ma.L2                    -0.0203      0.053     -0.386      0.700      -0.123       0.083
ma.L3                    -0.1016      0.012     -8.182      0.000      -0.126      -0.077
sigma2                 1.145e+05   7754.888     14.771      0.000    9.94e+04     1.3e+05
===================================================================================
Ljung-Box (L1) (Q):                  10.98   Jarque-Bera (JB):                38.54
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               1.26   Skew:                             0.27
Prob(H) (two-sided):                  0.32   Kurtosis:                         4.94
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 21169.47175267092
Parameters Used: ((0, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(3, 2, 2)   Log Likelihood               -1734.319
Date:                            Sat, 27 Jan 2024   AIC                           3482.639
Time:                                    01:48:35   BIC                           3506.644
Sample:                                01-31-2000   HQIC                          3492.324
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    -9.0576    136.110     -0.067      0.947    -275.828     257.713
ar.L1                    -0.1362      0.182     -0.749      0.454      -0.493       0.220
ar.L2                     0.4509      0.173      2.610      0.009       0.112       0.790
ar.L3                    -0.1597      0.021     -7.556      0.000      -0.201      -0.118
ma.L1                     0.1935      0.189      1.023      0.306      -0.177       0.564
ma.L2                    -0.5210      0.176     -2.959      0.003      -0.866      -0.176
sigma2                 2.044e+05   7777.614     26.282      0.000    1.89e+05     2.2e+05
===================================================================================
Ljung-Box (L1) (Q):                  20.81   Jarque-Bera (JB):              2591.52
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.52   Skew:                            -1.01
Prob(H) (two-sided):                  0.00   Kurtosis:                        19.39
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 31375.703208282517
Parameters Used: ((3, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 228
No suitable model parameters found for ZIP Code 23233. Skipping...
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 3)   Log Likelihood               -1558.914
Date:                            Sat, 27 Jan 2024   AIC                           3127.829
Time:                                    01:48:57   BIC                           3144.975
Sample:                                01-31-2000   HQIC                          3134.747
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -90.1847     71.487     -1.262      0.207    -230.296      49.927
ma.L1                     0.2418      0.019     12.801      0.000       0.205       0.279
ma.L2                     0.0532      0.032      1.660      0.097      -0.010       0.116
ma.L3                    -0.2676      0.024    -11.284      0.000      -0.314      -0.221
sigma2                 3.812e+04   2524.872     15.098      0.000    3.32e+04    4.31e+04
===================================================================================
Ljung-Box (L1) (Q):                   7.49   Jarque-Bera (JB):                44.15
Prob(Q):                              0.01   Prob(JB):                         0.00
Heteroskedasticity (H):               0.32   Skew:                            -0.00
Prob(H) (two-sided):                  0.00   Kurtosis:                         5.16
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 20395.326799476592
Parameters Used: ((0, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(3, 2, 0)   Log Likelihood               -1645.706
Date:                            Sat, 27 Jan 2024   AIC                           3301.412
Time:                                    01:49:27   BIC                           3318.559
Sample:                                01-31-2000   HQIC                          3308.330
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -43.1310    171.831     -0.251      0.802    -379.913     293.651
ar.L1                     0.0614      0.015      4.138      0.000       0.032       0.091
ar.L2                     0.0186      0.038      0.487      0.626      -0.056       0.094
ar.L3                    -0.0909      0.011     -8.642      0.000      -0.111      -0.070
sigma2                 9.938e+04   6473.898     15.351      0.000    8.67e+04    1.12e+05
===================================================================================
Ljung-Box (L1) (Q):                  16.29   Jarque-Bera (JB):                52.33
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.39   Skew:                             0.21
Prob(H) (two-sided):                  0.00   Kurtosis:                         5.31
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 19185.175163527314
Parameters Used: ((3, 2, 0), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(3, 2, 1)   Log Likelihood               -1649.166
Date:                            Sat, 27 Jan 2024   AIC                           3310.332
Time:                                    01:49:58   BIC                           3330.908
Sample:                                01-31-2000   HQIC                          3318.634
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -113.3867    423.178     -0.268      0.789    -942.801     716.028
ar.L1                     0.6043      0.147      4.119      0.000       0.317       0.892
ar.L2                     0.0210      0.050      0.422      0.673      -0.077       0.119
ar.L3                    -0.1046      0.030     -3.469      0.001      -0.164      -0.045
ma.L1                    -0.5625      0.149     -3.778      0.000      -0.854      -0.271
sigma2                 1.046e+05   6510.552     16.064      0.000    9.18e+04    1.17e+05
===================================================================================
Ljung-Box (L1) (Q):                  13.61   Jarque-Bera (JB):               106.58
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.25   Skew:                             0.34
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.28
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 25189.13524399547
Parameters Used: ((3, 2, 1), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(3, 2, 0)   Log Likelihood               -1610.879
Date:                            Sat, 27 Jan 2024   AIC                           3231.759
Time:                                    01:50:34   BIC                           3248.906
Sample:                                01-31-2000   HQIC                          3238.677
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -92.7232    145.493     -0.637      0.524    -377.885     192.439
ar.L1                     0.1065      0.017      6.371      0.000       0.074       0.139
ar.L2                     0.0274      0.042      0.647      0.518      -0.056       0.110
ar.L3                    -0.1566      0.013    -12.048      0.000      -0.182      -0.131
sigma2                 6.956e+04   5028.146     13.833      0.000    5.97e+04    7.94e+04
===================================================================================
Ljung-Box (L1) (Q):                  11.93   Jarque-Bera (JB):                22.67
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.50   Skew:                            -0.09
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.53
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 23443.46184203669
Parameters Used: ((3, 2, 0), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 228
No suitable model parameters found for ZIP Code 23238. Skipping...
Zip code 23250 not found in DataFrame. Skipping...
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 3)   Log Likelihood               -1681.854
Date:                            Sat, 27 Jan 2024   AIC                           3373.707
Time:                                    01:50:57   BIC                           3390.854
Sample:                                01-31-2000   HQIC                          3380.625
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -172.1220    107.467     -1.602      0.109    -382.753      38.509
ma.L1                     0.0525      0.018      2.975      0.003       0.018       0.087
ma.L2                    -0.0491      0.039     -1.263      0.206      -0.125       0.027
ma.L3                    -0.0771      0.014     -5.544      0.000      -0.104      -0.050
sigma2                 1.403e+05   7902.895     17.753      0.000    1.25e+05    1.56e+05
===================================================================================
Ljung-Box (L1) (Q):                  12.64   Jarque-Bera (JB):               173.77
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               1.50   Skew:                            -0.19
Prob(H) (two-sided):                  0.08   Kurtosis:                         7.26
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 25133.0353809512
Parameters Used: ((0, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                      SARIMAX Results                                      
===========================================================================================
Dep. Variable:      Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:             SARIMAX(2, 2, 3)x(1, 0, [], 12)   Log Likelihood                -868.898
Date:                             Sat, 27 Jan 2024   AIC                           1753.797
Time:                                     01:51:17   BIC                           1775.616
Sample:                                 01-31-2012   HQIC                          1762.651
                                      - 07-31-2021                                         
Covariance Type:                               opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -104.7364    207.885     -0.504      0.614    -512.183     302.710
ar.L1                     1.6511      0.067     24.748      0.000       1.520       1.782
ar.L2                    -0.8869      0.061    -14.598      0.000      -1.006      -0.768
ma.L1                    -1.6439      0.070    -23.556      0.000      -1.781      -1.507
ma.L2                     0.8141      0.089      9.105      0.000       0.639       0.989
ma.L3                     0.0498      0.035      1.411      0.158      -0.019       0.119
ar.S.L12                  0.0107      0.028      0.379      0.704      -0.045       0.066
sigma2                 2.692e+05   3.57e+04      7.538      0.000    1.99e+05    3.39e+05
===================================================================================
Ljung-Box (L1) (Q):                  10.20   Jarque-Bera (JB):                 0.57
Prob(Q):                              0.00   Prob(JB):                         0.75
Heteroskedasticity (H):               1.11   Skew:                             0.03
Prob(H) (two-sided):                  0.76   Kurtosis:                         3.34
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 5612.53759802421
Parameters Used: ((2, 2, 3), (1, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 29
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1630.359
Date:                            Sat, 27 Jan 2024   AIC                           3272.718
Time:                                    01:51:41   BIC                           3293.294
Sample:                                01-31-2000   HQIC                          3281.020
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   189.5644    112.453      1.686      0.092     -30.840     409.969
ar.L1                    -0.2410      0.063     -3.820      0.000      -0.365      -0.117
ar.L2                    -0.8450      0.046    -18.263      0.000      -0.936      -0.754
ma.L1                     0.3419      0.062      5.501      0.000       0.220       0.464
ma.L2                     0.8592      0.056     15.442      0.000       0.750       0.968
sigma2                 8.529e+04   7010.920     12.166      0.000    7.16e+04     9.9e+04
===================================================================================
Ljung-Box (L1) (Q):                   2.48   Jarque-Bera (JB):                 3.47
Prob(Q):                              0.12   Prob(JB):                         0.18
Heteroskedasticity (H):               0.40   Skew:                            -0.18
Prob(H) (two-sided):                  0.00   Kurtosis:                         3.49
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 33858.14078130278
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
No suitable model parameters found for ZIP Code 23831. Skipping...
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(3, 2, 0)   Log Likelihood               -1663.895
Date:                            Sat, 27 Jan 2024   AIC                           3337.791
Time:                                    01:52:10   BIC                           3354.937
Sample:                                01-31-2000   HQIC                          3344.709
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -124.3742    161.123     -0.772      0.440    -440.170     191.421
ar.L1                     0.0361      0.016      2.200      0.028       0.004       0.068
ar.L2                     0.0299      0.047      0.641      0.522      -0.062       0.121
ar.L3                    -0.0655      0.010     -6.573      0.000      -0.085      -0.046
sigma2                 1.204e+05   7534.809     15.980      0.000    1.06e+05    1.35e+05
===================================================================================
Ljung-Box (L1) (Q):                  14.09   Jarque-Bera (JB):                83.99
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.18   Skew:                             0.17
Prob(H) (two-sided):                  0.00   Kurtosis:                         5.95
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 36725.99757501821
Parameters Used: ((3, 2, 0), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                      SARIMAX Results                                      
===========================================================================================
Dep. Variable:      Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:             SARIMAX(2, 2, 2)x(1, 0, [], 12)   Log Likelihood                -823.396
Date:                             Sat, 27 Jan 2024   AIC                           1660.792
Time:                                     01:52:29   BIC                           1679.884
Sample:                                 01-31-2012   HQIC                          1668.539
                                      - 07-31-2021                                         
Covariance Type:                               opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   550.2480    192.966      2.852      0.004     172.041     928.455
ar.L1                     1.2659      0.016     77.338      0.000       1.234       1.298
ar.L2                    -0.9804      0.018    -54.695      0.000      -1.016      -0.945
ma.L1                    -1.2940      0.091    -14.248      0.000      -1.472      -1.116
ma.L2                     0.9977      0.131      7.613      0.000       0.741       1.255
ar.S.L12                 -0.0351      0.059     -0.597      0.551      -0.150       0.080
sigma2                 1.207e+05    2.6e+04      4.648      0.000    6.98e+04    1.72e+05
===================================================================================
Ljung-Box (L1) (Q):                   8.01   Jarque-Bera (JB):                11.35
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               2.32   Skew:                             0.46
Prob(H) (two-sided):                  0.01   Kurtosis:                         4.24
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 10020.378276144726
Parameters Used: ((2, 2, 2), (1, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 29
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(3, 2, 2)   Log Likelihood               -1550.272
Date:                            Sat, 27 Jan 2024   AIC                           3114.544
Time:                                    01:52:49   BIC                           3138.549
Sample:                                01-31-2000   HQIC                          3124.229
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    97.5436    134.498      0.725      0.468    -166.067     361.155
ar.L1                     0.3225      0.185      1.740      0.082      -0.041       0.686
ar.L2                     0.3467      0.122      2.833      0.005       0.107       0.587
ar.L3                    -0.3033      0.025    -12.175      0.000      -0.352      -0.255
ma.L1                    -0.2132      0.204     -1.048      0.295      -0.612       0.186
ma.L2                    -0.2648      0.114     -2.329      0.020      -0.488      -0.042
sigma2                 4.035e+04   2209.441     18.265      0.000     3.6e+04    4.47e+04
===================================================================================
Ljung-Box (L1) (Q):                   4.78   Jarque-Bera (JB):               244.87
Prob(Q):                              0.03   Prob(JB):                         0.00
Heteroskedasticity (H):               0.50   Skew:                             0.15
Prob(H) (two-sided):                  0.00   Kurtosis:                         8.07
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 25985.785732745004
Parameters Used: ((3, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1721.688
Date:                            Sat, 27 Jan 2024   AIC                           3455.377
Time:                                    01:53:17   BIC                           3475.953
Sample:                                01-31-2000   HQIC                          3463.679
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -321.9088    609.412     -0.528      0.597   -1516.334     872.517
ar.L1                     0.5853      0.011     53.514      0.000       0.564       0.607
ar.L2                    -0.9830      0.012    -80.630      0.000      -1.007      -0.959
ma.L1                    -0.5716      0.013    -44.932      0.000      -0.597      -0.547
ma.L2                     0.9845      0.015     64.713      0.000       0.955       1.014
sigma2                 1.962e+05   1.38e+04     14.193      0.000    1.69e+05    2.23e+05
===================================================================================
Ljung-Box (L1) (Q):                  13.98   Jarque-Bera (JB):               140.06
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.25   Skew:                             0.26
Prob(H) (two-sided):                  0.00   Kurtosis:                         6.80
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 22567.94465812128
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
No suitable model parameters found for ZIP Code 23838. Skipping...
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:                           SARIMAX(2, 2, 2)   Log Likelihood                -833.075
Date:                            Sat, 27 Jan 2024   AIC                           1678.151
Time:                                    01:53:39   BIC                           1694.515
Sample:                                01-31-2012   HQIC                          1684.791
                                     - 07-31-2021                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   347.9511    193.205      1.801      0.072     -30.724     726.626
ar.L1                     0.9695      0.080     12.125      0.000       0.813       1.126
ar.L2                    -0.8688      0.071    -12.165      0.000      -1.009      -0.729
ma.L1                    -0.9294      0.098     -9.530      0.000      -1.120      -0.738
ma.L2                     0.8142      0.088      9.252      0.000       0.642       0.987
sigma2                 1.484e+05   2.26e+04      6.568      0.000    1.04e+05    1.93e+05
===================================================================================
Ljung-Box (L1) (Q):                   8.31   Jarque-Bera (JB):                 1.98
Prob(Q):                              0.00   Prob(JB):                         0.37
Heteroskedasticity (H):               2.50   Skew:                             0.32
Prob(H) (two-sided):                  0.01   Kurtosis:                         2.91
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 8302.709562144044
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 29
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:                           SARIMAX(3, 2, 0)   Log Likelihood                -831.338
Date:                            Sat, 27 Jan 2024   AIC                           1672.676
Time:                                    01:53:58   BIC                           1686.313
Sample:                                01-31-2012   HQIC                          1678.210
                                     - 07-31-2021                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   308.9869    130.739      2.363      0.018      52.743     565.231
ar.L1                     0.0184      0.036      0.511      0.610      -0.052       0.089
ar.L2                    -0.0229      0.048     -0.472      0.637      -0.118       0.072
ar.L3                    -0.1009      0.020     -5.132      0.000      -0.139      -0.062
sigma2                 1.311e+05   1.72e+04      7.644      0.000    9.75e+04    1.65e+05
===================================================================================
Ljung-Box (L1) (Q):                   2.88   Jarque-Bera (JB):                 0.78
Prob(Q):                              0.09   Prob(JB):                         0.68
Heteroskedasticity (H):               3.01   Skew:                             0.17
Prob(H) (two-sided):                  0.00   Kurtosis:                         3.23
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 6947.214703643515
Parameters Used: ((3, 2, 0), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 29
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                      SARIMAX Results                                       
============================================================================================
Dep. Variable:       Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:             SARIMAX(2, 2, 2)x(0, 0, [1], 12)   Log Likelihood                -842.676
Date:                              Sat, 27 Jan 2024   AIC                           1699.353
Time:                                      01:54:19   BIC                           1718.445
Sample:                                  01-31-2012   HQIC                          1707.100
                                       - 07-31-2021                                         
Covariance Type:                                opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   562.2392    132.213      4.253      0.000     303.106     821.373
ar.L1                     0.8642      0.118      7.347      0.000       0.634       1.095
ar.L2                    -0.7406      0.148     -5.007      0.000      -1.031      -0.451
ma.L1                    -0.7985      0.132     -6.057      0.000      -1.057      -0.540
ma.L2                     0.6375      0.178      3.582      0.000       0.289       0.986
ma.S.L12                 -0.0936      0.050     -1.863      0.062      -0.192       0.005
sigma2                 1.745e+05   2.78e+04      6.278      0.000     1.2e+05    2.29e+05
===================================================================================
Ljung-Box (L1) (Q):                   5.15   Jarque-Bera (JB):                 0.04
Prob(Q):                              0.02   Prob(JB):                         0.98
Heteroskedasticity (H):               1.93   Skew:                            -0.03
Prob(H) (two-sided):                  0.05   Kurtosis:                         2.93
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 6888.561476671278
Parameters Used: ((2, 2, 2), (0, 0, 1, 12))
len(exog_forecast) Forecast time period in months: 29
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(3, 2, 3)   Log Likelihood               -1504.189
Date:                            Sat, 27 Jan 2024   AIC                           3024.377
Time:                                    01:54:45   BIC                           3051.812
Sample:                                01-31-2000   HQIC                          3035.446
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    65.9317     33.907      1.945      0.052      -0.524     132.387
ar.L1                     0.3210      0.049      6.496      0.000       0.224       0.418
ar.L2                    -0.0147      0.050     -0.298      0.766      -0.112       0.082
ar.L3                     0.2451      0.033      7.341      0.000       0.180       0.311
ma.L1                     0.0157      0.065      0.241      0.809      -0.112       0.143
ma.L2                     0.1345      0.056      2.383      0.017       0.024       0.245
ma.L3                    -0.9170      0.065    -14.063      0.000      -1.045      -0.789
sigma2                 2.222e+04   1851.068     12.005      0.000    1.86e+04    2.58e+04
===================================================================================
Ljung-Box (L1) (Q):                   0.62   Jarque-Bera (JB):               121.30
Prob(Q):                              0.43   Prob(JB):                         0.00
Heteroskedasticity (H):               0.92   Skew:                            -0.48
Prob(H) (two-sided):                  0.72   Kurtosis:                         6.44
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 30727.23859212034
Parameters Used: ((3, 2, 3), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 58
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:                           SARIMAX(3, 2, 0)   Log Likelihood                -840.987
Date:                            Sat, 27 Jan 2024   AIC                           1691.975
Time:                                    01:55:02   BIC                           1705.612
Sample:                                01-31-2012   HQIC                          1697.508
                                     - 07-31-2021                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   307.6362    156.365      1.967      0.049       1.166     614.106
ar.L1                     0.0974      0.032      3.036      0.002       0.035       0.160
ar.L2                    -0.0146      0.050     -0.295      0.768      -0.112       0.083
ar.L3                    -0.1330      0.020     -6.726      0.000      -0.172      -0.094
sigma2                 1.449e+05    1.9e+04      7.644      0.000    1.08e+05    1.82e+05
===================================================================================
Ljung-Box (L1) (Q):                   7.22   Jarque-Bera (JB):                 0.96
Prob(Q):                              0.01   Prob(JB):                         0.62
Heteroskedasticity (H):               2.75   Skew:                             0.12
Prob(H) (two-sided):                  0.00   Kurtosis:                         3.38
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 8686.579368178305
Parameters Used: ((3, 2, 0), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 29
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 3)   Log Likelihood               -1572.023
Date:                            Sat, 27 Jan 2024   AIC                           3154.046
Time:                                    01:55:25   BIC                           3171.193
Sample:                                01-31-2000   HQIC                          3160.964
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   145.2551     89.194      1.629      0.103     -29.562     320.073
ma.L1                     0.1010      0.025      4.050      0.000       0.052       0.150
ma.L2                    -0.0277      0.042     -0.658      0.511      -0.110       0.055
ma.L3                    -0.1699      0.016    -10.553      0.000      -0.201      -0.138
sigma2                 5.034e+04   2611.490     19.274      0.000    4.52e+04    5.55e+04
===================================================================================
Ljung-Box (L1) (Q):                   3.24   Jarque-Bera (JB):               176.34
Prob(Q):                              0.07   Prob(JB):                         0.00
Heteroskedasticity (H):               1.50   Skew:                            -0.33
Prob(H) (two-sided):                  0.08   Kurtosis:                         7.26
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 48293.93050314988
Parameters Used: ((0, 2, 3), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
Zip code 23801 not found in DataFrame. Skipping...
len(exog): 229
No suitable model parameters found for ZIP Code 23803. Skipping...
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                      SARIMAX Results                                      
===========================================================================================
Dep. Variable:      Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:             SARIMAX(2, 2, 3)x(1, 0, [], 12)   Log Likelihood               -1462.514
Date:                             Sat, 27 Jan 2024   AIC                           2941.028
Time:                                     01:55:59   BIC                           2968.462
Sample:                                 01-31-2000   HQIC                          2952.097
                                      - 02-28-2019                                         
Covariance Type:                               opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    52.6226     21.727      2.422      0.015      10.038      95.207
ar.L1                     0.1975      0.054      3.640      0.000       0.091       0.304
ar.L2                    -0.1620      0.053     -3.084      0.002      -0.265      -0.059
ma.L1                     0.2205      0.051      4.300      0.000       0.120       0.321
ma.L2                     0.3188      0.054      5.904      0.000       0.213       0.425
ma.L3                    -0.6771      0.052    -12.919      0.000      -0.780      -0.574
ar.S.L12                  0.1631      0.042      3.891      0.000       0.081       0.245
sigma2                 1.534e+04    938.044     16.351      0.000    1.35e+04    1.72e+04
===================================================================================
Ljung-Box (L1) (Q):                   0.15   Jarque-Bera (JB):                37.27
Prob(Q):                              0.70   Prob(JB):                         0.00
Heteroskedasticity (H):               2.84   Skew:                             0.08
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.97
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 35953.24920508907
Parameters Used: ((2, 2, 3), (1, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 58
Zip code 23806 not found in DataFrame. Skipping...
len(exog): 143
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 143
len(train): 143
len(exog_train): 143
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  143
Model:                           SARIMAX(2, 2, 0)   Log Likelihood               -1031.656
Date:                            Sat, 27 Jan 2024   AIC                           2071.313
Time:                                    01:56:27   BIC                           2083.108
Sample:                                02-28-2009   HQIC                          2076.106
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   243.9892    275.341      0.886      0.376    -295.670     783.648
ar.L1                     0.0257      0.024      1.077      0.282      -0.021       0.072
ar.L2                     0.0296      0.063      0.469      0.639      -0.094       0.153
sigma2                 1.318e+05    1.3e+04     10.166      0.000    1.06e+05    1.57e+05
===================================================================================
Ljung-Box (L1) (Q):                  11.91   Jarque-Bera (JB):                 8.25
Prob(Q):                              0.00   Prob(JB):                         0.02
Heteroskedasticity (H):               3.18   Skew:                             0.06
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.18
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 57916.31214670818
Parameters Used: ((2, 2, 0), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 144
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 144
len(train): 144
len(exog_train): 144
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  144
Model:                           SARIMAX(1, 2, 0)   Log Likelihood               -1018.322
Date:                            Sat, 27 Jan 2024   AIC                           2042.643
Time:                                    01:56:57   BIC                           2051.511
Sample:                                01-31-2009   HQIC                          2046.247
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   320.8284    192.624      1.666      0.096     -56.708     698.365
ar.L1                     0.0308      0.019      1.599      0.110      -0.007       0.068
sigma2                 9.729e+04   9518.663     10.221      0.000    7.86e+04    1.16e+05
===================================================================================
Ljung-Box (L1) (Q):                  17.14   Jarque-Bera (JB):                 7.82
Prob(Q):                              0.00   Prob(JB):                         0.02
Heteroskedasticity (H):               4.59   Skew:                             0.23
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.05
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 50730.195400616
Parameters Used: ((1, 2, 0), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 3)   Log Likelihood               -1662.174
Date:                            Sat, 27 Jan 2024   AIC                           3338.348
Time:                                    01:57:24   BIC                           3362.353
Sample:                                01-31-2000   HQIC                          3348.033
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    14.9850     93.639      0.160      0.873    -168.545     198.515
ar.L1                     0.2090      0.177      1.182      0.237      -0.138       0.556
ar.L2                    -0.6427      0.119     -5.396      0.000      -0.876      -0.409
ma.L1                    -0.2011      0.181     -1.112      0.266      -0.556       0.153
ma.L2                     0.5863      0.135      4.340      0.000       0.322       0.851
ma.L3                    -0.0588      0.023     -2.595      0.009      -0.103      -0.014
sigma2                 1.181e+05   1.09e+04     10.833      0.000    9.67e+04    1.39e+05
===================================================================================
Ljung-Box (L1) (Q):                  12.61   Jarque-Bera (JB):                 0.28
Prob(Q):                              0.00   Prob(JB):                         0.87
Heteroskedasticity (H):               0.56   Skew:                            -0.02
Prob(H) (two-sided):                  0.01   Kurtosis:                         3.17
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 30642.805442283272
Parameters Used: ((2, 2, 3), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(3, 2, 3)   Log Likelihood               -1665.149
Date:                            Sat, 27 Jan 2024   AIC                           3346.297
Time:                                    01:57:42   BIC                           3373.732
Sample:                                01-31-2000   HQIC                          3357.366
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    80.7849     90.593      0.892      0.373     -96.775     258.345
ar.L1                     0.3084      0.060      5.102      0.000       0.190       0.427
ar.L2                    -0.1674      0.068     -2.447      0.014      -0.302      -0.033
ar.L3                     0.3640      0.050      7.237      0.000       0.265       0.463
ma.L1                    -0.0560      0.065     -0.866      0.387      -0.183       0.071
ma.L2                     0.1119      0.068      1.646      0.100      -0.021       0.245
ma.L3                    -0.7718      0.054    -14.400      0.000      -0.877      -0.667
sigma2                 9.096e+04   4237.094     21.467      0.000    8.27e+04    9.93e+04
===================================================================================
Ljung-Box (L1) (Q):                   1.15   Jarque-Bera (JB):               322.94
Prob(Q):                              0.28   Prob(JB):                         0.00
Heteroskedasticity (H):               0.75   Skew:                             0.47
Prob(H) (two-sided):                  0.21   Kurtosis:                         8.75
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 29896.873523035134
Parameters Used: ((3, 2, 3), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 58
len(exog): 163
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 163
len(train): 163
len(exog_train): 163
len(test): 41
len(exog_test): 41
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  163
Model:                           SARIMAX(3, 2, 2)   Log Likelihood               -1164.501
Date:                            Sat, 27 Jan 2024   AIC                           2343.002
Time:                                    01:58:09   BIC                           2364.572
Sample:                                01-31-2007   HQIC                          2351.761
                                     - 07-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   222.9454    160.333      1.391      0.164     -91.301     537.192
ar.L1                     0.9148      0.036     25.137      0.000       0.843       0.986
ar.L2                    -0.9087      0.033    -27.187      0.000      -0.974      -0.843
ar.L3                    -0.0459      0.030     -1.522      0.128      -0.105       0.013
ma.L1                    -0.9423      0.022    -42.618      0.000      -0.986      -0.899
ma.L2                     0.9179      0.016     56.546      0.000       0.886       0.950
sigma2                 9.808e+04   9594.982     10.222      0.000    7.93e+04    1.17e+05
===================================================================================
Ljung-Box (L1) (Q):                   6.53   Jarque-Bera (JB):                 5.43
Prob(Q):                              0.01   Prob(JB):                         0.07
Heteroskedasticity (H):               0.91   Skew:                            -0.44
Prob(H) (two-sided):                  0.73   Kurtosis:                         3.19
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 18209.488332015782
Parameters Used: ((3, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 41
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 0)   Log Likelihood               -1795.965
Date:                            Sat, 27 Jan 2024   AIC                           3595.930
Time:                                    01:58:40   BIC                           3602.789
Sample:                                01-31-2000   HQIC                          3598.697
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -520.1203    657.662     -0.791      0.429   -1809.114     768.874
sigma2                 4.059e+05   1.45e+04     27.941      0.000    3.77e+05    4.34e+05
===================================================================================
Ljung-Box (L1) (Q):                  26.75   Jarque-Bera (JB):              1317.32
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.22   Skew:                            -0.97
Prob(H) (two-sided):                  0.00   Kurtosis:                        14.61
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 75051.33980243167
Parameters Used: ((0, 2, 0), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 58
len(exog): 214
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 214
len(train): 214
len(exog_train): 214
len(test): 54
len(exog_test): 54
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  214
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1660.531
Date:                            Sat, 27 Jan 2024   AIC                           3333.062
Time:                                    01:59:02   BIC                           3353.201
Sample:                                09-30-2001   HQIC                          3341.201
                                     - 06-30-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    60.6387    157.227      0.386      0.700    -247.521     368.798
ar.L1                     0.7296      0.011     66.842      0.000       0.708       0.751
ar.L2                    -0.9991      0.008   -128.337      0.000      -1.014      -0.984
ma.L1                    -0.7262      0.021    -33.997      0.000      -0.768      -0.684
ma.L2                     0.9988      0.045     22.117      0.000       0.910       1.087
sigma2                 3.282e+05      0.024   1.39e+07      0.000    3.28e+05    3.28e+05
===================================================================================
Ljung-Box (L1) (Q):                   4.99   Jarque-Bera (JB):                14.54
Prob(Q):                              0.03   Prob(JB):                         0.00
Heteroskedasticity (H):               0.68   Skew:                            -0.04
Prob(H) (two-sided):                  0.11   Kurtosis:                         4.28
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 9.24e+23. Standard errors may be unstable.
Test RMSE: 32909.600181263246
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 54
len(exog): 216
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 216
len(train): 216
len(exog_train): 216
len(test): 54
len(exog_test): 54
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  216
Model:                           SARIMAX(2, 2, 1)   Log Likelihood               -1820.580
Date:                            Sat, 27 Jan 2024   AIC                           3651.160
Time:                                    01:59:25   BIC                           3667.990
Sample:                                07-31-2001   HQIC                          3657.960
                                     - 06-30-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   246.0719    505.979      0.486      0.627    -745.629    1237.773
ar.L1                     0.9016      0.052     17.305      0.000       0.799       1.004
ar.L2                    -0.1225      0.020     -6.280      0.000      -0.161      -0.084
ma.L1                    -0.9239      0.043    -21.573      0.000      -1.008      -0.840
sigma2                 1.391e+06   1.03e+05     13.490      0.000    1.19e+06    1.59e+06
===================================================================================
Ljung-Box (L1) (Q):                   8.98   Jarque-Bera (JB):                17.69
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.17   Skew:                            -0.07
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.40
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 21035.532753516614
Parameters Used: ((2, 2, 1), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 54
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 57
len(exog_test): 57
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 3)   Log Likelihood               -1747.952
Date:                            Sat, 27 Jan 2024   AIC                           3509.905
Time:                                    01:59:52   BIC                           3533.910
Sample:                                02-29-2000   HQIC                          3519.590
                                     - 03-31-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag    20.3909    160.960      0.127      0.899    -295.085     335.867
ar.L1                     1.7853      0.048     37.114      0.000       1.691       1.880
ar.L2                    -0.9439      0.045    -21.014      0.000      -1.032      -0.856
ma.L1                    -1.7616      0.053    -33.199      0.000      -1.866      -1.658
ma.L2                     0.8784      0.058     15.129      0.000       0.765       0.992
ma.L3                     0.0369      0.021      1.796      0.073      -0.003       0.077
sigma2                  2.75e+05   1.92e+04     14.345      0.000    2.37e+05    3.13e+05
===================================================================================
Ljung-Box (L1) (Q):                  17.16   Jarque-Bera (JB):                78.71
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               1.38   Skew:                             0.44
Prob(H) (two-sided):                  0.17   Kurtosis:                         5.74
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 34526.35942773662
Parameters Used: ((2, 2, 3), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 57
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 1)   Log Likelihood               -1794.426
Date:                            Sat, 27 Jan 2024   AIC                           3598.853
Time:                                    02:00:22   BIC                           3615.999
Sample:                                01-31-2000   HQIC                          3605.771
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -55.2746    142.149     -0.389      0.697    -333.881     223.332
ar.L1                     0.7724      0.346      2.235      0.025       0.095       1.450
ar.L2                    -0.0547      0.018     -2.971      0.003      -0.091      -0.019
ma.L1                    -0.7463      0.343     -2.174      0.030      -1.419      -0.074
sigma2                 3.901e+05   3.32e+04     11.755      0.000    3.25e+05    4.55e+05
===================================================================================
Ljung-Box (L1) (Q):                  16.38   Jarque-Bera (JB):                16.28
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               2.15   Skew:                             0.53
Prob(H) (two-sided):                  0.00   Kurtosis:                         3.76
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 24501.123350545706
Parameters Used: ((2, 2, 1), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                      SARIMAX Results                                       
============================================================================================
Dep. Variable:       Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:             SARIMAX(3, 2, 3)x(0, 0, [1], 12)   Log Likelihood               -1618.211
Date:                              Sat, 27 Jan 2024   AIC                           3254.423
Time:                                      02:00:48   BIC                           3285.287
Sample:                                  01-31-2000   HQIC                          3266.875
                                       - 02-28-2019                                         
Covariance Type:                                opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -40.3036     41.721     -0.966      0.334    -122.075      41.468
ar.L1                     0.2616      0.048      5.417      0.000       0.167       0.356
ar.L2                     0.1341      0.058      2.325      0.020       0.021       0.247
ar.L3                     0.1691      0.036      4.747      0.000       0.099       0.239
ma.L1                     0.0544      0.049      1.109      0.268      -0.042       0.151
ma.L2                     0.0291      0.055      0.529      0.597      -0.079       0.137
ma.L3                    -0.8118      0.050    -16.218      0.000      -0.910      -0.714
ma.S.L12                  0.0933      0.033      2.812      0.005       0.028       0.158
sigma2                 4.943e+04   3469.585     14.246      0.000    4.26e+04    5.62e+04
===================================================================================
Ljung-Box (L1) (Q):                   0.29   Jarque-Bera (JB):                45.20
Prob(Q):                              0.59   Prob(JB):                         0.00
Heteroskedasticity (H):               0.93   Skew:                            -0.25
Prob(H) (two-sided):                  0.76   Kurtosis:                         5.12
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 34865.83270484767
Parameters Used: ((3, 2, 3), (0, 0, 1, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
len(exog_forecast) Forecast time period in months: 58
len(exog): 1
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\fromnumeric.py:3715: RuntimeWarning: Degrees of freedom <= 0 for slice
  return _methods._var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:223: RuntimeWarning: invalid value encountered in divide
  arrmean = um.true_divide(arrmean, div, out=arrmean, casting='unsafe',
C:\Users\rsingh\anaconda3\lib\site-packages\numpy\core\_methods.py:257: RuntimeWarning: invalid value encountered in double_scalars
  ret = ret.dtype.type(ret / rcount)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for ARMA and trend. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:866: UserWarning: Too few observations to estimate starting parameters for seasonal ARMA. All parameters except for variances will be set to zeros.
  warn('Too few observations to estimate starting parameters%s.'
cutoff: 1
len(train): 1
len(exog_train): 1
len(test): 0
len(exog_test): 0
Error processing ZIP Code 23894: Insufficient data points for prediction.. Skipping...
len(exog): 201
No suitable model parameters found for ZIP Code 22546. Skipping...
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
  self._init_dates(dates, freq)
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1749.991
Date:                            Sat, 27 Jan 2024   AIC                           3511.982
Time:                                    02:01:20   BIC                           3532.558
Sample:                                01-31-2000   HQIC                          3520.283
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   136.1875    103.256      1.319      0.187     -66.191     338.566
ar.L1                     0.9746      0.014     67.353      0.000       0.946       1.003
ar.L2                    -0.9719      0.014    -70.849      0.000      -0.999      -0.945
ma.L1                    -0.9770      0.017    -58.763      0.000      -1.010      -0.944
ma.L2                     0.9597      0.019     51.509      0.000       0.923       0.996
sigma2                 2.275e+05    1.2e+04     18.897      0.000    2.04e+05    2.51e+05
===================================================================================
Ljung-Box (L1) (Q):                  14.75   Jarque-Bera (JB):               127.52
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.65   Skew:                            -0.35
Prob(H) (two-sided):                  0.06   Kurtosis:                         6.60
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 28528.432115722422
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
len(exog_forecast) Forecast time period in months: 58
len(exog): 145
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 145
len(train): 145
len(exog_train): 145
len(test): 36
len(exog_test): 36
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  145
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1087.032
Date:                            Sat, 27 Jan 2024   AIC                           2186.064
Time:                                    02:01:40   BIC                           2203.841
Sample:                                12-31-2008   HQIC                          2193.288
                                     - 12-31-2020                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   308.6638    277.720      1.111      0.266    -235.657     852.985
ar.L1                     1.0434      0.014     75.527      0.000       1.016       1.070
ar.L2                    -0.9800      0.014    -72.035      0.000      -1.007      -0.953
ma.L1                    -1.0330      0.016    -64.620      0.000      -1.064      -1.002
ma.L2                     0.9743      0.016     59.889      0.000       0.942       1.006
sigma2                 2.019e+05   2.12e+04      9.502      0.000     1.6e+05    2.44e+05
===================================================================================
Ljung-Box (L1) (Q):                  18.27   Jarque-Bera (JB):                 0.59
Prob(Q):                              0.00   Prob(JB):                         0.75
Heteroskedasticity (H):               1.91   Skew:                             0.15
Prob(H) (two-sided):                  0.03   Kurtosis:                         3.10
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 81679.44448985926
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 214
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 214
len(train): 214
len(exog_train): 214
len(test): 53
len(exog_test): 53
Error processing ZIP Code 23015: Provided exogenous values are not of the appropriate shape. Required (54, 1), got (53, 1).. Skipping...
len(exog): 213
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 213
len(train): 213
len(exog_train): 213
len(test): 53
len(exog_test): 53
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  213
Model:                           SARIMAX(2, 2, 2)   Log Likelihood               -1554.589
Date:                            Sat, 27 Jan 2024   AIC                           3121.178
Time:                                    02:02:38   BIC                           3141.289
Sample:                                11-30-2001   HQIC                          3129.307
                                     - 07-31-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   233.4051    180.803      1.291      0.197    -120.962     587.772
ar.L1                     1.1219      0.027     41.520      0.000       1.069       1.175
ar.L2                    -0.9173      0.032    -29.016      0.000      -0.979      -0.855
ma.L1                    -1.1451      0.033    -34.778      0.000      -1.210      -1.081
ma.L2                     0.8847      0.040     21.907      0.000       0.806       0.964
sigma2                 1.495e+05   1.17e+04     12.733      0.000    1.27e+05    1.73e+05
===================================================================================
Ljung-Box (L1) (Q):                  17.31   Jarque-Bera (JB):                27.42
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.36   Skew:                             0.31
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.65
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 45193.67908305381
Parameters Used: ((2, 2, 2), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 53
len(exog): 115
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 115
len(train): 115
len(exog_train): 115
len(test): 29
len(exog_test): 29
                                      SARIMAX Results                                       
============================================================================================
Dep. Variable:       Zillow Home Value Index (ZHVI)   No. Observations:                  115
Model:             SARIMAX(3, 2, 2)x(0, 0, [1], 12)   Log Likelihood                -873.595
Date:                              Sat, 27 Jan 2024   AIC                           1763.191
Time:                                      02:02:59   BIC                           1785.010
Sample:                                  01-31-2012   HQIC                          1772.045
                                       - 07-31-2021                                         
Covariance Type:                                opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   506.4348    337.177      1.502      0.133    -154.421    1167.290
ar.L1                     1.1208      0.073     15.323      0.000       0.977       1.264
ar.L2                    -0.8820      0.061    -14.465      0.000      -1.001      -0.762
ar.L3                     0.0037      0.028      0.134      0.893      -0.050       0.058
ma.L1                    -1.1257      0.070    -16.180      0.000      -1.262      -0.989
ma.L2                     0.8472      0.059     14.354      0.000       0.732       0.963
ma.S.L12                 -0.0484      0.056     -0.871      0.384      -0.157       0.061
sigma2                 2.461e+05   3.31e+04      7.439      0.000    1.81e+05    3.11e+05
===================================================================================
Ljung-Box (L1) (Q):                  18.57   Jarque-Bera (JB):                 2.38
Prob(Q):                              0.00   Prob(JB):                         0.30
Heteroskedasticity (H):               0.87   Skew:                             0.14
Prob(H) (two-sided):                  0.68   Kurtosis:                         2.35
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 65095.620076409585
Parameters Used: ((3, 2, 2), (0, 0, 1, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
len(exog_forecast) Forecast time period in months: 29
len(exog): 139
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 139
len(train): 139
len(exog_train): 139
len(test): 35
len(exog_test): 35
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  139
Model:                           SARIMAX(0, 2, 0)   Log Likelihood               -1044.534
Date:                            Sat, 27 Jan 2024   AIC                           2093.067
Time:                                    02:03:27   BIC                           2098.907
Sample:                                07-31-2009   HQIC                          2095.441
                                     - 01-31-2021                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -20.6350    398.325     -0.052      0.959    -801.338     760.068
sigma2                 2.461e+05   2.66e+04      9.253      0.000    1.94e+05    2.98e+05
===================================================================================
Ljung-Box (L1) (Q):                  24.73   Jarque-Bera (JB):                 1.75
Prob(Q):                              0.00   Prob(JB):                         0.42
Heteroskedasticity (H):               2.00   Skew:                             0.13
Prob(H) (two-sided):                  0.02   Kurtosis:                         3.49
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 46743.15578745808
Parameters Used: ((0, 2, 0), (0, 0, 0, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 35
len(exog): 143
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
cutoff: 143
len(train): 143
len(exog_train): 143
len(test): 36
len(exog_test): 36
                                      SARIMAX Results                                       
============================================================================================
Dep. Variable:       Zillow Home Value Index (ZHVI)   No. Observations:                  143
Model:             SARIMAX(2, 2, 3)x(1, 0, [1], 12)   Log Likelihood                   0.000
Date:                              Sat, 27 Jan 2024   AIC                             18.000
Time:                                      02:04:04   BIC                             44.539
Sample:                                  02-28-2009   HQIC                            28.784
                                       - 12-31-2020                                         
Covariance Type:                                opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   157.7360         -0       -inf      0.000     157.736     157.736
ar.L1                     0.0001   3.68e-12    3.9e+07      0.000       0.000       0.000
ar.L2                     0.9999         -0       -inf      0.000       1.000       1.000
ma.L1                     0.4847         -0       -inf      0.000       0.485       0.485
ma.L2                    -0.9998         -0        inf      0.000      -1.000      -1.000
ma.L3                    -0.4850         -0        inf      0.000      -0.485      -0.485
ar.S.L12                  1.0000         -0       -inf      0.000       1.000       1.000
ma.S.L12                 -1.0000         -0        inf      0.000      -1.000      -1.000
sigma2                 1.268e+07         -0       -inf      0.000    1.27e+07    1.27e+07
===================================================================================
Ljung-Box (L1) (Q):                    nan   Jarque-Bera (JB):                  nan
Prob(Q):                               nan   Prob(JB):                          nan
Heteroskedasticity (H):                nan   Skew:                              nan
Prob(H) (two-sided):                   nan   Kurtosis:                          nan
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number    inf. Standard errors may be unstable.
Test RMSE: 262077.7380650973
Parameters Used: ((2, 2, 3), (1, 0, 1, 12))
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\mlemodel.py:2979: RuntimeWarning: divide by zero encountered in divide
  return self.params / self.bse
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\stattools.py:1346: RuntimeWarning: invalid value encountered in divide
  test_statistic = numer_squared_sum / denom_squared_sum
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\stattools.py:681: RuntimeWarning: invalid value encountered in divide
  acf = avf[: nlags + 1] / avf[0]
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
len(exog_forecast) Forecast time period in months: 36
len(exog): 144
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 144
len(train): 144
len(exog_train): 144
len(test): 36
len(exog_test): 36
                                      SARIMAX Results                                       
============================================================================================
Dep. Variable:       Zillow Home Value Index (ZHVI)   No. Observations:                  144
Model:             SARIMAX(2, 2, 2)x(1, 0, [1], 12)   Log Likelihood               -1099.300
Date:                              Sat, 27 Jan 2024   AIC                           2214.600
Time:                                      02:04:39   BIC                           2238.247
Sample:                                  01-31-2009   HQIC                          2224.209
                                       - 12-31-2020                                         
Covariance Type:                                opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   205.9959    411.249      0.501      0.616    -600.037    1012.028
ar.L1                     1.0412      0.009    117.280      0.000       1.024       1.059
ar.L2                    -0.9994      0.008   -123.711      0.000      -1.015      -0.984
ma.L1                    -1.0391      0.036    -28.549      0.000      -1.110      -0.968
ma.L2                     0.9993      0.066     15.036      0.000       0.869       1.130
ar.S.L12                  0.9563      0.581      1.647      0.099      -0.181       2.094
ma.S.L12                 -0.9586      0.575     -1.668      0.095      -2.085       0.168
sigma2                 2.668e+05      0.350   7.62e+05      0.000    2.67e+05    2.67e+05
===================================================================================
Ljung-Box (L1) (Q):                  14.18   Jarque-Bera (JB):                 0.63
Prob(Q):                              0.00   Prob(JB):                         0.73
Heteroskedasticity (H):               1.81   Skew:                            -0.08
Prob(H) (two-sided):                  0.04   Kurtosis:                         2.71
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
[2] Covariance matrix is singular or near-singular, with condition number 6.11e+21. Standard errors may be unstable.
Test RMSE: 86882.1214587689
Parameters Used: ((2, 2, 2), (1, 0, 1, 12))
len(exog_forecast) Forecast time period in months: 36
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
                                      SARIMAX Results                                       
============================================================================================
Dep. Variable:       Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:             SARIMAX(2, 2, 2)x(1, 0, [1], 12)   Log Likelihood               -1791.315
Date:                              Sat, 27 Jan 2024   AIC                           3598.631
Time:                                      02:05:27   BIC                           3626.066
Sample:                                  01-31-2000   HQIC                          3609.700
                                       - 02-28-2019                                         
Covariance Type:                                opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag   -88.0867    155.133     -0.568      0.570    -392.142     215.969
ar.L1                     0.9664      0.011     86.564      0.000       0.945       0.988
ar.L2                    -0.9660      0.010    -92.730      0.000      -0.986      -0.946
ma.L1                    -0.9851      0.013    -77.625      0.000      -1.010      -0.960
ma.L2                     0.9618      0.013     76.676      0.000       0.937       0.986
ar.S.L12                  0.7979      0.090      8.838      0.000       0.621       0.975
ma.S.L12                 -0.7573      0.103     -7.338      0.000      -0.960      -0.555
sigma2                  3.27e+05   2.01e+04     16.235      0.000    2.88e+05    3.67e+05
===================================================================================
Ljung-Box (L1) (Q):                  14.46   Jarque-Bera (JB):                34.24
Prob(Q):                              0.00   Prob(JB):                         0.00
Heteroskedasticity (H):               0.25   Skew:                            -0.39
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.73
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 31957.01274524892
Parameters Used: ((2, 2, 2), (1, 0, 1, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 0)   Log Likelihood               -1772.982
Date:                            Sat, 27 Jan 2024   AIC                           3549.964
Time:                                    02:06:11   BIC                           3556.823
Sample:                                01-31-2000   HQIC                          3552.731
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -192.7414    155.673     -1.238      0.216    -497.854     112.371
sigma2                 3.332e+05   2.56e+04     13.017      0.000    2.83e+05    3.83e+05
===================================================================================
Ljung-Box (L1) (Q):                   4.59   Jarque-Bera (JB):                12.67
Prob(Q):                              0.03   Prob(JB):                         0.00
Heteroskedasticity (H):               0.48   Skew:                            -0.22
Prob(H) (two-sided):                  0.00   Kurtosis:                         4.07
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 31534.32477773312
Parameters Used: ((0, 2, 0), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
len(exog): 230
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.
  warn('Non-stationary starting autoregressive parameters'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\statespace\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.
  warn('Non-invertible starting MA parameters found.'
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\base\model.py:604: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals
  warnings.warn("Maximum Likelihood optimization failed to "
C:\Users\rsingh\anaconda3\lib\site-packages\statsmodels\tsa\base\tsa_model.py:471: ValueWarning: No frequency information was provided, so inferred frequency M will be used.
  self._init_dates(dates, freq)
cutoff: 230
len(train): 230
len(exog_train): 230
len(test): 58
len(exog_test): 58
                                     SARIMAX Results                                      
==========================================================================================
Dep. Variable:     Zillow Home Value Index (ZHVI)   No. Observations:                  230
Model:                           SARIMAX(0, 2, 0)   Log Likelihood               -1696.497
Date:                            Sat, 27 Jan 2024   AIC                           3396.995
Time:                                    02:06:52   BIC                           3403.853
Sample:                                01-31-2000   HQIC                          3399.762
                                     - 02-28-2019                                         
Covariance Type:                              opg                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
financial_crisis_flag  -172.3566    115.907     -1.487      0.137    -399.530      54.816
sigma2                 1.701e+05   1.21e+04     14.038      0.000    1.46e+05    1.94e+05
===================================================================================
Ljung-Box (L1) (Q):                   3.26   Jarque-Bera (JB):                28.42
Prob(Q):                              0.07   Prob(JB):                         0.00
Heteroskedasticity (H):               0.81   Skew:                            -0.23
Prob(H) (two-sided):                  0.36   Kurtosis:                         4.67
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).
Test RMSE: 33830.63100442656
Parameters Used: ((0, 2, 0), (0, 0, 0, 12))
len(exog_forecast) Forecast time period in months: 58
In [19]:
print(results_df)
    Zip_Code      Test_RMSE  Forecast_%_Appreciation         Parameters Used
0      23089   33254.056059                19.569822  (2, 2, 1, 0, 0, 0, 12)
1      23093   39470.578370                64.105328  (2, 2, 3, 0, 0, 0, 12)
2      23102   63255.216466                51.521151  (2, 2, 2, 0, 0, 0, 12)
3      23103            NaN                      NaN  (1, 2, 1, 0, 0, 0, 12)
4      23106   28930.367662                53.022332  (3, 2, 2, 0, 0, 0, 12)
..       ...            ...                      ...                     ...
67     23038  262077.738065              -100.000000  (2, 2, 3, 1, 0, 1, 12)
68     23039   86882.121459                54.077651  (2, 2, 2, 1, 0, 1, 12)
69     23047   31957.012745                15.929120  (2, 2, 2, 1, 0, 1, 12)
70     23059   31534.324778                18.690472  (0, 2, 0, 0, 0, 0, 12)
71     23060   33830.631004                22.661455  (0, 2, 0, 0, 0, 0, 12)

[72 rows x 4 columns]
In [20]:
results_df
Out[20]:
Zip_Code Test_RMSE Forecast_%_Appreciation Parameters Used
0 23089 33254.056059 19.569822 (2, 2, 1, 0, 0, 0, 12)
1 23093 39470.578370 64.105328 (2, 2, 3, 0, 0, 0, 12)
2 23102 63255.216466 51.521151 (2, 2, 2, 0, 0, 0, 12)
3 23103 NaN NaN (1, 2, 1, 0, 0, 0, 12)
4 23106 28930.367662 53.022332 (3, 2, 2, 0, 0, 0, 12)
... ... ... ... ...
67 23038 262077.738065 -100.000000 (2, 2, 3, 1, 0, 1, 12)
68 23039 86882.121459 54.077651 (2, 2, 2, 1, 0, 1, 12)
69 23047 31957.012745 15.929120 (2, 2, 2, 1, 0, 1, 12)
70 23059 31534.324778 18.690472 (0, 2, 0, 0, 0, 0, 12)
71 23060 33830.631004 22.661455 (0, 2, 0, 0, 0, 0, 12)

72 rows × 4 columns

In [21]:
# Step 2: Merge with results_df
# Ensure that the 'Zip_Code' column in both dataframes are of the same data type
gdf['Zip_Code'] = gdf['Zip_Code'].astype(int)# Modify the column name if different in your shapefile
results_df['Zip_Code'] = results_df['Zip_Code'].astype(int)
merged_gdf = gdf.merge(results_df, on='Zip_Code', how='right')
In [22]:
print(results_df.describe())
           Zip_Code      Test_RMSE  Forecast_%_Appreciation
count     72.000000      66.000000                66.000000
mean   23295.638889   36415.547918                33.795687
std      305.920974   33876.146731                23.895277
min    23005.000000    5529.342245              -100.000000
25%    23099.750000   21335.605330                22.899958
50%    23183.000000   30269.839483                34.480273
75%    23236.250000   39379.317944                45.771065
max    23894.000000  262077.738065                80.817558
In [23]:
print(results_df.info())
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 72 entries, 0 to 71
Data columns (total 4 columns):
 #   Column                   Non-Null Count  Dtype  
---  ------                   --------------  -----  
 0   Zip_Code                 72 non-null     int32  
 1   Test_RMSE                66 non-null     float64
 2   Forecast_%_Appreciation  66 non-null     float64
 3   Parameters Used          72 non-null     object 
dtypes: float64(2), int32(1), object(1)
memory usage: 2.1+ KB
None
In [24]:
print(results_df.head())  # First 5 rows
print(results_df.tail())  # Last 5 rows
   Zip_Code     Test_RMSE  Forecast_%_Appreciation         Parameters Used
0     23089  33254.056059                19.569822  (2, 2, 1, 0, 0, 0, 12)
1     23093  39470.578370                64.105328  (2, 2, 3, 0, 0, 0, 12)
2     23102  63255.216466                51.521151  (2, 2, 2, 0, 0, 0, 12)
3     23103           NaN                      NaN  (1, 2, 1, 0, 0, 0, 12)
4     23106  28930.367662                53.022332  (3, 2, 2, 0, 0, 0, 12)
    Zip_Code      Test_RMSE  Forecast_%_Appreciation         Parameters Used
67     23038  262077.738065              -100.000000  (2, 2, 3, 1, 0, 1, 12)
68     23039   86882.121459                54.077651  (2, 2, 2, 1, 0, 1, 12)
69     23047   31957.012745                15.929120  (2, 2, 2, 1, 0, 1, 12)
70     23059   31534.324778                18.690472  (0, 2, 0, 0, 0, 0, 12)
71     23060   33830.631004                22.661455  (0, 2, 0, 0, 0, 0, 12)
In [25]:
sorted_df = results_df.sort_values(by='Forecast_%_Appreciation', ascending=False)
sorted_df
Out[25]:
Zip_Code Test_RMSE Forecast_%_Appreciation Parameters Used
24 23224 18024.145008 80.817558 (1, 2, 3, 0, 0, 0, 12)
62 23011 81679.444490 72.864093 (2, 2, 2, 0, 0, 0, 12)
65 23027 65095.620076 65.240710 (3, 2, 2, 0, 0, 1, 12)
1 23093 39470.578370 64.105328 (2, 2, 3, 0, 0, 0, 12)
66 23030 46743.155787 61.052270 (0, 2, 0, 0, 0, 0, 12)
... ... ... ... ...
7 23113 NaN NaN (2, 2, 2, 1, 0, 0, 12)
9 23117 NaN NaN (0, 2, 3, 0, 0, 0, 12)
12 23129 NaN NaN (0, 2, 0, 0, 0, 0, 12)
60 23894 NaN NaN (0, 2, 0, 0, 0, 0, 12)
63 23015 NaN NaN (0, 2, 0, 0, 0, 0, 12)

72 rows × 4 columns

In [ ]:
 
In [ ]:
 
In [26]:
results_df.head()
Out[26]:
Zip_Code Test_RMSE Forecast_%_Appreciation Parameters Used
0 23089 33254.056059 19.569822 (2, 2, 1, 0, 0, 0, 12)
1 23093 39470.578370 64.105328 (2, 2, 3, 0, 0, 0, 12)
2 23102 63255.216466 51.521151 (2, 2, 2, 0, 0, 0, 12)
3 23103 NaN NaN (1, 2, 1, 0, 0, 0, 12)
4 23106 28930.367662 53.022332 (3, 2, 2, 0, 0, 0, 12)
In [27]:
merged_gdf.head()
Out[27]:
ZCTA5CE10 Zip_Code CLASSFP10 MTFCC10 FUNCSTAT10 ALAND10 AWATER10 INTPTLAT10 INTPTLON10 geometry Test_RMSE Forecast_%_Appreciation Parameters Used
0 23089 23089 B5 G6350 S 156945786 16563560 +37.4557955 -076.9035007 POLYGON ((-76.98172 37.48980, -76.98163 37.490... 33254.056059 19.569822 (2, 2, 1, 0, 0, 0, 12)
1 23093 23093 B5 G6350 S 540280167 5234667 +38.0041674 -078.0400574 MULTIPOLYGON (((-78.12450 38.09174, -78.12438 ... 39470.578370 64.105328 (2, 2, 3, 0, 0, 0, 12)
2 23102 23102 B5 G6350 S 76839503 2667817 +37.7081193 -077.8286536 POLYGON ((-77.88998 37.66425, -77.88986 37.664... 63255.216466 51.521151 (2, 2, 2, 0, 0, 0, 12)
3 23103 23103 B5 G6350 S 96822168 3577185 +37.6480344 -077.7236401 POLYGON ((-77.82239 37.61005, -77.82196 37.610... NaN NaN (1, 2, 1, 0, 0, 0, 12)
4 23106 23106 B5 G6350 S 69705539 1245598 +37.7161066 -077.2015109 POLYGON ((-77.27119 37.75150, -77.27111 37.751... 28930.367662 53.022332 (3, 2, 2, 0, 0, 0, 12)
In [28]:
# Step 3: Visualize the Map
fig, ax = plt.subplots(figsize=(10, 10))
# Plotting gdf_bkg as a white background
gdf_bkg.plot(ax=ax, color='white', edgecolor='black')
merged_gdf.plot(column='Test_RMSE', ax=ax, legend=True, cmap='viridis')
ax.set_title("Test RMSE by Zip Code")
plt.show()
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
In [31]:
# Step 3: Visualize the Map
fig, ax = plt.subplots(figsize=(10, 10))
# Plotting gdf_bkg as a white background
gdf_bkg.plot(ax=ax, color='white', edgecolor='black')
merged_gdf.plot(column='Forecast_%_Appreciation', ax=ax, legend=True, cmap='viridis')
ax.set_title("Forecast_%_Appreciation by ZipCode")
plt.show()
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
In [ ]:
 
In [32]:
path1 = r"C:\Users\rsingh\OneDrive - PlanRVA\Documents\DataHub-Rishabh\Base locality Boundary\Loc_Boundary_RTC.shp"
gdf_counties = gpd.read_file(path1)
In [33]:
# Plotting
fig, ax = plt.subplots(figsize=(10, 10))
gdf_counties.plot(ax=ax, color='White', edgecolor='black', linewidth=0.5)
Out[33]:
<AxesSubplot:>
In [34]:
import geopandas as gpd
import matplotlib.pyplot as plt

# Merge your geodataframe with your results_df
merged_gdf = gdf.merge(results_df, on='Zip_Code')

# Plotting
fig, ax = plt.subplots(figsize=(10, 10))

# Plotting the main data
merged_gdf.plot(column='Forecast_%_Appreciation', ax=ax, legend=True, cmap='viridis')

# Overlaying the county boundaries with transparent fill
gdf_counties.plot(ax=ax, color='none', edgecolor='black', linewidth=1)

# Setting plot limits to the extent of gdf_counties
minx, miny, maxx, maxy = gdf_counties.total_bounds
ax.set_xlim(minx, maxx)
ax.set_ylim(miny, maxy)

ax.set_title("Forecast_%_Appreciation by ZipCode")
plt.show()
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
In [35]:
import geopandas as gpd
import matplotlib.pyplot as plt

# Merge your geodataframe with your results_df
merged_gdf = gdf.merge(results_df, on='Zip_Code')

# Plotting
fig, ax = plt.subplots(figsize=(10, 10))

# First, plot the county boundaries with white fill. This covers the entire plot area.
gdf_counties.plot(ax=ax, color='white', edgecolor='black', linewidth=0.5)

# Then plot the main data on top. Only areas within gdf_counties boundaries will be visible.
merged_gdf.plot(column='Forecast_%_Appreciation', ax=ax, legend=True, cmap='viridis')

# Setting plot limits to the extent of gdf_counties
minx, miny, maxx, maxy = gdf_counties.total_bounds
ax.set_xlim(minx, maxx)
ax.set_ylim(miny, maxy)

ax.set_title("Forecast_%_Appreciation by ZipCode")
plt.show()
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
In [36]:
import geopandas as gpd
import matplotlib.pyplot as plt

# Merge your geodataframe with your results_df
merged_gdf = gdf.merge(results_df, on='Zip_Code')

# Clipping merged_gdf with gdf_counties
clipped_gdf = gpd.clip(merged_gdf, gdf_counties)

# Plotting
fig, ax = plt.subplots(figsize=(10, 10))

# Plot the county boundaries
gdf_counties.plot(ax=ax, color='none', edgecolor='black', linewidth=0.5)

# Plot the clipped data
clipped_gdf.plot(column='Forecast_%_Appreciation', ax=ax, legend=True, cmap='viridis')

# Setting plot limits to the extent of gdf_counties, if desired
minx, miny, maxx, maxy = gdf_counties.total_bounds
ax.set_xlim(minx, maxx)
ax.set_ylim(miny, maxy)

ax.set_title("Forecast_%_Appreciation by ZipCode")
plt.show()
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
In [37]:
import geopandas as gpd
import matplotlib.pyplot as plt

# Merge your geodataframe with your results_df
merged_gdf = gdf.merge(results_df, on='Zip_Code')

# Clipping merged_gdf with gdf_counties
clipped_gdf = gpd.clip(merged_gdf, gdf_counties)

# Plotting
fig, ax = plt.subplots(figsize=(10, 10))

# Plot the county boundaries
gdf_counties.plot(ax=ax, color='none', edgecolor='black', linewidth=0.5)

# Plot the clipped data
clipped_gdf.plot(column='Test_RMSE', ax=ax, legend=True, cmap='viridis')

# Setting plot limits to the extent of gdf_counties, if desired
minx, miny, maxx, maxy = gdf_counties.total_bounds
ax.set_xlim(minx, maxx)
ax.set_ylim(miny, maxy)

ax.set_title("Test RMSE by Zip Code")
plt.show()
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
C:\Users\rsingh\anaconda3\lib\site-packages\geopandas\plotting.py:48: ShapelyDeprecationWarning: The 'type' attribute is deprecated, and will be removed in the future. You can use the 'geom_type' attribute instead.
  if geom is not None and geom.type.startswith(prefix) and not geom.is_empty:
In [ ]:
 
In [ ]:
## Next Steps: Forecast ahead - 5 Years, 10 Years ..
In [ ]:
# Save the plot to a file
    if not os.path.exists(save_plot_dir):
        os.makedirs(save_plot_dir)
    plt.savefig(os.path.join(save_plot_dir, f'ZHVI_forecast_{zip_code}.png'))

    plt.show()
In [ ]:
def model(df, order, seasonal_order):
    cutoff = round(df.shape[0]*0.9)
    train = df['Zillow Home Value Index (ZHVI)'][:cutoff].dropna()
    exog_train = df.dropna()['financial_crisis_flag'][:cutoff]
    test = df['Zillow Home Value Index (ZHVI)'][cutoff:]
    exog_test = np.zeros(len(test)).reshape(-1, 1)


    #Experimenting with different optimization methods (e.g., 'nm', 'bfgs', 'lbfgs', etc, and maxiter=500
    model = SARIMAX(endog=train, exog=exog_train, order=order, seasonal_order=seasonal_order, freq='M', method='lbfgs', maxiter=500).fit(disp=False)
    #model = SARIMAX(endog=train, exog=exog_train, order=order, seasonal_order=seasonal_order, freq='M').fit()
    y_hat_train = model.predict(start=train.index[2], typ='levels')
    y_hat_test = model.predict(start=test.index[0], end=test.index[-1], typ='levels', exog=exog_test)

    print(model.summary())
    print(f'Test RMSE: {rmse(test, y_hat_test)}')
    print(f'Parameters Used: {order, seasonal_order}')

    fig, ax = plt.subplots(figsize=(12,8))
    ax.plot(train, label='train')
    ax.plot(test, label='test')
    ax.plot(y_hat_train, label='train prediction')
    ax.plot(y_hat_test, label='test prediction')
    ax.set_ylabel('Zillow Home Value Index (ZHVI)', fontsize=12)
    ax.set_xlabel('Year', fontsize=12)
    plt.legend()
    plt.show()
    
    # Save the plot to a file
    save_plot_dir = r"C:\Users\rsingh\OneDrive - PlanRVA\Documents\Time_Series_GrowthProject\plots"
    if not os.path.exists(save_plot_dir):
        os.makedirs(save_plot_dir)
    plt.savefig(os.path.join(save_plot_dir, f'ZHVI_forecast_{zip_code}.png'))

    plt.show()
    
    test_rmse = rmse(test, y_hat_test)
    exog_forecast = np.zeros(12).reshape(-1, 1)
    forecast = model.forecast(steps=12, exog=exog_forecast)
    # Last observed value in the TRAIN set
    last_train_value = train.iloc[-1]
    forecast_return = (forecast[-1] - last_train_value) / last_train_value * 100

    return test_rmse, forecast_return